Vibrating on notes near the nut
I have trouble vibrating on those notes close to the nut. Especially the Bb in a G-minor G-D-Bb-G chord. Even as single notes, I feel like I don't have enough room and my knuckles keep knocking the pegs. As a double stop, my index finger's first knuckle locks and doesn't vibrate at all because it feels like I need a fair amount of pressure to stop the string, otherwise the Bb sounds like I haven't pressed the string down all the way.
Are your pegs at a good angle to minimise this problem? If not, you may need to lift your hand frame up a bit, so that you're more over the string and not reaching back too much.
What type of shoulder rest should I use?
It is indeed more difficult to vibrate there. It will improve as your overall vibrato improves. Very important is the flexibility of the last joint (the joint closest to the tip of the finger). If you find it is not flexible, you can work on that using the Rivarde exercise (look that up). What I do find strange is that you write that you need a lot of pressure close to the nut. Since the string is very close to the fingerboard there, you actually do not need much pressure there.
As Jean says, you should not have to use a lot of left hand pressure anywhere and especially there. You may not need to use much vibrato on a chord if any at all, and players tend to use far too much anyway. A small finger vibrato is all that is required. Too much vib messes up intonation and is bad for ear training. Go for a pure sound which can be enhanced where necessary with some vibrato.
I'll tell you how: make your 1st finger at a much more shallow angle than usual, almost flat on the fingerboard. You can also think of it as blocking the string with the pad of the finger, rather than exclusively with the tip. This should immediately make both arm vibrato and wrist vibrato accessible, even in the case of the g-minor chord you mentioned, even if you're using more finger pressure than you should be (speaking of which, you might wanna check your nut height with a luthier to see if it's sufficiently low to allow for minimal pressure on low notes). In the g-minor chord, make sure both the 1st and 2nd fingers are at a shallow angle so they can synchronize properly.
"Since the string is very close to the fingerboard there, you actually do not need much pressure there."
Our best vibrato is with the 3rd and 2nd fingers. The 4th is narrower. The first is in the awkward "square" form. Instead, whenever possible move to 3rd position, 3rd finger.
As a violist with small hands (a bit masochist?) I often move the hand back into half position just to vibrate on a well rounded, flexible index finger. The contact with the string is then nearer the nail, giving a clearer tone even if I don't press right down to the fingerboard.
Well, OP never responded so I guess he doesn't care.
Hi Erik, the nut was too high on my violin.
Did fixing the nut also prevent your knuckles from knocking the pegs?
yes, the knocking of the pegs was from the extra effort I exerted to try and get a vibrato.