MrYikes, tension that develops while playing is one problem.  Tension you bring into a practice or playing session is another.

I deal with the latter before any practice by stretching my hands for a few minutes while I plan out the variable parts of practice.  Then some very basic things to limber the upper body.. Neck circles, shoulder rolls, trunk twists, shaking out the wrists and hands, that sort of thing.  Then pick up the instrument and bow, bring the violin to playing position, and then consciously relax and take a couple of deep breaths before raising the bow.. I find that helps a bit.

My current practice routine for violin:

5 minutes of open string bowing with long full bow strokes.  I make them slower as i start to warm up, seeing how slow I can draw the bow and still get good sound.

5 minutes of open string bowing in the rhythm of interest at the moment (one of those variable parts i mentioned).  That can be a "standard" like 4/4, 3/4, 6/8, 7/8.. Or it can be the rhythm of some song or piece where I have noted I am clumsier than I like.  

5 minutes of open string bowing as doublestops.  It can be long strokes or a rhythm of interest.  

Then I move on to practising scales of interest against a simple click or beat (like a metronome) but with a short reference note (Like a C for the key of C Major or minor, for example) on every 4th beat.  That way the drone isn't here as a constant reference, but it is often enough that I can keep checking my intonation against it while working on playing to a beat.  As I get comfortable and get the playing on the beat precise enough for my liking I start multiplying how many notes I play to each beat.  I push that a bit to see how many I can play per beat while still staying right dead on the beat and keeping my intonation decent.  

5 min per scale chosen for the day, 3 scales, so it is another 15 minutes.

Then I improvise to backing tracks where I can use those scales I just practised, but in a more creative way.  Sometimes I do 5-8 min with a backing track for each scale, or if I'm feeling gutsy, I may work out of only one scale for about 20 minutes.  That is actually a rather long time to improvise, just making melody up as you go along.  It gives your creativity quite a workout, if you are actually trying to some up with things to play that not only fit, but sound interesting and good. LOL

That's my usual minimum basic practice.  The focus/purpose of it is to do a reasonable amount of work on basic skills and techniques, but the improvisation section is for working to develop fluidity and fluency.  As I am using those words here, "Fluidity" is what I am calling the ability to move from any note in a scale to any other note comfortably.  "Fluency" is knowing what that move will actually sound like before doing it.  The only way I know to improve those is experience, and what has usually worked best for me to gain that experience is improvisation.  It is what I have found to work for me, I don't know if it would be the best choice for you or anyone else. 

So there ya go, MrYikes, I hope it helps.