A couple of thoughts when reading your post:
First - this is pretty normal behavior for that age group. Some toddlers go through it more than others, but hitting/biting/grabbing are all completely normal behaviors. You are handling it exactly the way I did, and it will take a lot of repetition, and redirection. Telling him over and over to play gently, gentle touch, empathizing with his feelings (it's so hard to wait your turn, it's really upsetting when someone grabs from you, etc.), and redirecting him to another activity/toy. Often times you may have to gently take him into another room to do something else. They are pretty young to be playing together for any lenght of time without an adult right there anyhow. But when you have a kid who is going through a serious biting or hitting phase, you can't really take your eyes off of them around other kids.
As far as dealing with your sister, I would forget about thinking in terms of backgrounds. You are going to deal with a lot of different parenting styles, and they are not always going to be related to a person's background. There are going to be a lot of ECE specialists who will tell you to use harsh discipline, for example. I would instead focus on "this is what works for us." No need to debate who is right. I would, however, make it clear that she is not to discipline your child, and that she can come get you if there is a problem.
And the reality may be that the kids can't play together much without you there. It will probably get better as they get older, but maybe not. There are certain playdates that are more exhausting than others, and I just try to minimize those.