I'd talk to the coach about it. They will let you know which skills are okay for your child to practice at home. I think it probably depends on the parent and child, too. For example, I think my daughter's coach might be more okay with my daughter practicing at home because I used to do birthday parties at the gym and know how to teach some basic skills already. I'm not very good with "form", though, so I usually ask the coach for pointers on those things.
I wouldn't recommending helping with anything your daughter isn't ready for and hasn't already practiced extensively at the gym, though. Or anything that she doesn't want to do. It should be fun and comfortable. Not only should she be physically and mentally ready, but she should be interested, and you should also have talked to the coach first.
That said, there's a wide range of opinions on this subject. I think your decision should be based on the coach you're daughter is working with, as they will know *you* and *your* child better as well as what works best for *them*. Every child is different, and different gyms/coaches will have different ideals.
Oh... to answer...
IMO, pushing your child is when you encourage them to do things they aren't ready to or don't want to do. Pushing your child is making them feel like they have to do something to feel loved/accepted/make their parent happy. I guess at sometimes gymnastics becomes a competitive sport, but IMO, it should be fun. When they do get to that stage where it's competitive, the only one who should be "pushing them" is themselves, and they can get *support* from their coach and parents... but it does no good to push someone--they have to want it for themselves.
HTH!