Sounds pretty normal to me, at least up to a point. 3 and 17 months here, and not that different; except the 17 month old stands up to himself a bit better.
We handle it in a very straightforward manner. Any toy grabbing means immediate removal of that toy from play for the day, unless that would excessively harm the wronged party if there is a clear wronged party. In that case, an equivalent toy is gone for the day that belongs to the party in the wrong. However, we tend towards removing the toy that is the proximate cause of conflict, because it often defuses the conflict more effectively (they will just go back to fighting over the same toy otherwise).
It's not always perfectly effective, but it does tend to work fairly well on balance. We also try to work with the older child on empathy: explaining to him how his younger brother feels, and reminding him how he feels when his brother takes things from him.
You can also help by training your older daughter to have positive interactions with her younger sibling. Train her to give her younger sister toys, rather than take them away. When our older boy wants a toy the younger one has, we reinforce that he should offer a trade. We point out when his younger brother is sad and what he can do to help - offer a toy, pick up a fallen item, etc. This all reinforces, positively, things he can do that make his brother happy, without too much negative reinforcement. Negative reinforcement is the biggest problem here, I would suggest: if all the older one knows is negative things related to the younger one, well, that has an obvious outcome.