Hi, @LoveStrings, welcome to the forum. Hope you have fun here.

Sounds like you went back into performing in public a little too quickly and possibly picked up your daughter's anxiety, so that now, you have a strong dose of anxiety attached to playing. (Since you didn't mention this only happening during public performances, I'm assuming it's attached to playing, not publicly performing.)

If we could have several long conversations, so that I knew your personal psychology, I could make better suggestions, but... I'll throw out several ideas and hopefully one will work for you (and if more than one do, great.)

First off, the physical. This is obviously a mental problem, but sometimes it's easier to tackle these things backwards and work on the physical side and let that fix the mental side.

If you can find one, take a self-hypnosis class. It's a useful skill to have, and it it doesn't do anything else for you, it will teach you how to relax at will.

One of the techniques I learned when I took it (way too many years ago) was:

• Get comfortable.
• Deliberately tense the muscles in one part of your body. It's easiest to keep track of things if you move from one end to the other, so start with your toes.
• Clench them, then relax them. Do that a couple or three times the first time to teach yourself. Further on down the road, just once for each group of muscles is enough.
• Then do the feet
• Then pull the feet back (working the shins, stretching the calves), then the opposite (push the feet down, contracting the calves, stretching the shins) After all of these, remember to relax the muscle as completely as possible. (And leave the ones you've already done nice and boneless, too.)
• Then do the thighs (both directions)
• Then clench and release the buttocks, then the belly
• Then the fingers (first making a fist, relaxing, then spreading them wide, then relaxing)
• Then move up the arm in a similar way to how you did the legs.
• Then clench and release the chest muscles and the back muscles
• Then do the front, back, and each side of the neck.
• Then the jaw (don't overdo clenching your teeth or opening your jaw - just do it enough to get a sense of tension in the muscles.)
• Do your ears, if you can move them (some people can, some can't)
• Do the eyes, eyebrows and brow
• If you can find any other muscles in the head you can do this with do them.
• You should now be pretty boneless and relaxed all over your body. Enjoy it for as long as you wish, then go on about your day.

After you've learned how to do it, and practiced it a few times, that will take about 2 minutes.  It should make you much more skilled at relaxing muscles deliberately when you need to.

Mental:

This is going to be a complete grab bag of ideas. The physical stuff above I'm fairly sure will be of some use to practically anyone. The stuff below...  I'm sure some of the ideas will help some people. I'm not sure any of them will help you personally - all I can do is put stuff out there and hope.

• Try reason - if you DID connect your daughter's anxiety to it (along with some of your own, I'm sure), notice that you've been playing for two years since then, and have hardly died even a little bit.  (Reason is a 50 kg weakling dealing with 150 kg boxers when emotions are involved, so don't get your hopes up too high for this one.   (Translation for 'Merkins:  98lb weakling among 300 lb linebackers)
• Substitute a good association for a bad one. You right now have that episode with your daughter attached to playing. Connect up stuff from when you 8 years old, preferably really positive ones, even better, ones that involved performing in public. If you had a recital go really well, that would be ideal. Pull that memory up and hold it in your mind every time you start to practice (and perform in public.)
• Imagine things being much, much, much worse. You're in a huge, prestigious venue (Albert Hall, maybe? - sorry, don't know the UK that well), with whatever would be the worst possible audience for you. Famous people, hostile people, highly critical people, etc.  Every time you make a mistake, an article of clothing disappears. If all the clothing is gone, each mistake schedules you for a torture of some kind.  And then you'll be shunned by everyone you know, and exiled to Antarctica (where your violin will break after about an hour.) Now look out at your real audience (or practice room) and relax.
• Humor - Don't know if you've seen the Addam's family movies. In the second one, Grandma-ma is telling the older children "Are you worried because you think that when a new child is born, one of the older children is killed? That's just not true!" And then in an obviously sad and disappointed voice, "Not anymore...".  If you find that as funny as I do, think of what you're afraid might happen to you (awfulize it some, like the above), and think to yourself, "Not anymore..."   (Here's the scene: )
• Courageous thoughts - Anxiety is obviously a species of fear. As one book title had it, "Feel the Fear and do it anyway." Tension is an attempt to suppress the fear. Stop trying to do that, and feel it in it full glory (or inglory, if you prefer). Fear is a funny animal - it will chase you up until the point you start chasing it. Then it runs away from you. If you start trying to pin it down and fully experience what, exactly, it is you're afraid of, you are very likely to find that the fear just up and evaporates.  No fear = no anxiety = no tension.

Change of subject - vibrato

First off, you're going to have to do something about the tension first. Most of vibrato requires things to be loose and flexible. One or two muscles are making rhythmic pulling motions, and a couple of muscles are under light tension to hold your finger down (lightly). Pretty much everything else needs to be free to move easily.

Somebody on the forum (sorry, I've forgotten who should get the credit) did us all a huge favor a couple of weeks ago and pointed us to this video on vibrato:   Best video on vibrato I've ever seen. He's a rather dry speaker, but VERY good information.

My teacher gave me a good vibrato exercise:

Put your right hand in front of you, relaxed. Put the tip of your left thumb in the center of the palm. (If your right hand is relaxed, that will be the bottom of a pit.)

Put whatever finger you want to practice with on the back of your right hand, opposite the thumb. I recommend the middle finger, because it reaches most easily, and this is primarily for exercising the wrist or arm muscles that will move the hand, but there's probably some value in practicing with different fingers from time to time.

Keeping the thumb in the same spot, move the tip of the finger up and down the back of the left hand, parallel to the tendons. (My finger naturally lands between the tendons for the middle and ring finger, so those are the two I go between). You should be using just enough force that the skin on the back of your hand moves along with your fingertip.

Things you can do to make it more like an actual violin:

Tilt the right hand down.

Turn the right hand so that the back is more up than out.

Move both hands to the left some. (If you move them both out near where a the fingerboard will be, it will be very realistic, but very awkward. I'd suggest a compromise that comfortable.)

This exercise has a one huge advantage - you have the stuff necessary to do it with you wherever you go.

Another one that's handy, but requires the violin:

The hardest thing about vibrato for many people is that it's an awkward, unfamiliar motion.  So start out with something less awkward and more familiar, and work up to the vibrato position.

I recommend doing the above hand exercise first. You get to where you can can do the back and forth motion and know what it feels like very quickly with that. (And by very quickly, I mean a couple of minutes or less.)

Now take the violin and hold it it somewhat like a ukelele. The idea is to have the part of the fingerboard that you're working with right in front of you, so that your left arm isn't having to be stretched out to the side at all. It's working straight ahead.

Do that same exercise as you did with the hand on the neck. Your thumb is on the back, your fingertip is on one of the strings. Do all four fingers on all four strings. Notice how you have to change things to account for the curvature of the fingerboard, especially on the G string.

Now move the violin to the left a few inches, and repeat the whole exercise.

Keep doing that until you're all the way out in normal position.

As you move further out, you'll probably need more practice time with each new position before you're comfortable with it. Get comfortable with it before moving to the next one.

Don't plan on moving from the starting position to normal playing position in one session. It will take as long as it takes. You don't have to move two inches at a time, either. If you want to just move a finger's width, so that you can say you're making progress, that's fine. As long as you're getting more comfortable with being closer and closer to normal playing position, you're going to get there.

1st position in normal playing position is the hardest for vibrato. I'd recommend aiming at something easier as your first target.

4th finger - I'd need to hear more about what problems you're having to comment much on that.

4th finger was something sudden for me. I hadn't been using it much, and I had one piece that I just could not seem to speed up to anything like proper speed to save my life, and one day I tried playing it with 4th finger. It was so much easier it wasn't funny. Most of the difficulty of increasing the speed was a lot of string changes, and using the 4th finger eliminated 3/4s of them.  So I tend to use it a lot now, and it hasn't been that hard for me. But I have fairly big hands, which might be why it's not hard. 

The one trick I've learned to keep it from getting painful is to make sure I get enough of my hand over it that I can keep the finger curved. That makes it a good bit stronger.  If you have small hands and that keeps you from being able to curve the finger, I understand the problem, but I'm afraid I don't have a fix for you.

Hope something in all this helped