Focus on the left hand and do vibrato without the bow. Your right hand can help support the violin and this will help your left arm stay free.
Start with 1st finger B on A-string, then while you vibrate on this note, place 2nd finger G# on E-string, then 3rd finger D# on A-string, then 4th finger B on E-string.
After you can do this on two strings, practice your continuous vibrato on the same string.
Also do this on other pairs of strings.
The reason for placing fingers on neighbouring strings rather than on the same string is to encourage an open left-hand shape.
NOTE - This is a silent exercise, there is no audio.
Pre-Vibrato - Knock Peg Double Stop
Scores - Continuous Vibrato - violin & viola