@maudmaud

Your hand looks like it is positioned well.  I’m still working on my vibrato—it’s been a long journey.

There is a lot of advice out there about vibrato.  My teacher has given me suggestions, & some exercises to try.  As I’ve tried different things (her suggestions as well as those of others) with me demonstrating what I was practicing, we would discuss it.  However, she’s been hesitant to tell me specifically how to do it.  I believe she thinks each individual has to discover what works best; that it is a very individual thing.

So, I won’t try to tell you how you should specifically do it, but I can describe my vibrato journey.  Since I’m in the middle of it, it may or may not be helpful.

Tension is definitely the enemy.  As AndrewH noted, this and thumb position is important—I had a tendency of moving my thumb back (toward the peg box), which makes the vibrato motion difficult.  

To release tension in my thumb, I would place my finger down on the string that I was going to play, & then lift my thumb off the neck.  Then I would try the vibrato motion on that finger, and then place my thumb back on the neck where it best facilitated the motion. 

It’s made me rethink my hand positioning all the time (a good thing), and how I balance my hand to get a good, smooth motion.  You may find that you need to position your hand a little differently than you have been doing as you practice it on different strings, different fingers, etc.,.

After practicing for a while with exercises & scales (I started as you did, with a metronome), I’ve tried to incorporate it in music I’m already practicing.  I started using it on longer notes (half note, dotted half note, etc.,) played with the 3^rd finger (I’ve found my 3^rd finger has been the easiest).  Now I might use it in a specific phrase incorporating more notes (more fingers) where it seems to flow easily.  Not quite all the way there yet, but I’m working on it.