I have some experience with reading notes (piano)
And how important is a quality instrument?
My parents are not willing to invest more than $100-150 in a violin, and any other costs it may have.

My sister used to play the violin and she never really got into it. I have her old violin..but it just sounds awful and scratchy, even when she plays it.
Also, she has been holding her violin wrong for so long that it shifted her jaw. I don't want that to happen to me.

I wouldn't, unless you really love the instrument.

I played violin for over 15 years, played in orchestras, performed on stage.
It's an instrument that's hard to learn and hard to master. It'll wear out your left ear, it'll screw up your neck and your jaws. I don't touch the violin anymore, and I don't see much reason for anyone to learn the instrument to be honest. I love the sound of violins, but I'd rather listen than play.

Keyboard on the other hand, I can't imagine not being able to play it whenever I want. It's permanently a part of my life. So unless somebody has the same relationship to violin as I do to keyboard, I wouldn't.

If you really want to play violin in a perfect manner , then it is not a tough work , as you said that yo can also play piano very well, if you have strong determination to learn anything then you can do it . So go for it my dear , you can also join some coaching classes for this .