You cannot expect a 3 year old to want to play with a 17 month old. It's nice if they do, but what you are describing is quite usual.
I would provide the little one with toys and leave her to play as she pleases.
Ask the older girl what she wants to do? Play, and if so, let her choose the toys herself (except those reserved for little one), or help you?
I know it takes longer to dust the room if you have a 3 year old crawling around with a duster, rubbing enthusiastically at the chair legs, but she will love helping you.
If she wants to play, let her do so. If she pushes her sister, stop her gently and say something like, "No dear, that hurts", move her away from her sister and try to distract the big one into playing something else.
Don't scold her, just gently say no.
If she persists in wanting whatever toy her sister is playing with, I would let her choose the toys she wants first, and give the younger one the rest. After that take a toy away from the big girl if she takes it from her sister and give it back to the little one.
It will eventually dawn upon her that grandma is not going to let her have her own way all the time, and she will love you for setting understandable boundaries.