Great question. It is not ideal for any sort of tension to pop up in the hand even if the case is necessary. Sounds like that might be what you are doing here. This causes restriction in the rest of your hand to play fast, do vibrato, and become fluid to play the violin in general (can actually translate to difficulty keeping the right hand relaxed as well). My suggestion would be to work on exercises where your 4th finger is not being forced to find the note, which typically requires a higher hand. I’ve had at least 3-4 students before with a short pinky and this has always been helpful. The other thing to work on is not reaching for notes, and focus on keeping your hand back while placing each note. This might seem impossible if your hand is tense, but dooable if you have no sort of muscle restriction.
The biggest thing with 4th finger efficiency is flexibility and hand height. Forcing the reach/stretch is only going to make things worse. The other suggestion I would make (if nothing else works) is to get a smaller sized violin (3/4 size). A few of my students have done that and found that the smaller distance that is required makes a difference for them. Hope this helps!