Personally I would contact someone about installing whatever is necessary to properly secure a child safety seat in your RV near your captains seats. The front seats in your coach were not designed for a child safety seat.
As far as doing the things you ask in a moving RV, most of us just use common sense. Legally the laws vary from state to state and most do not cover Class A RV's. Even commercial buses allow people to get up and move around. There are times when it is not practical to be up and moving around, like in a city, twisting roads, mountain roads, inclement weather, etc. There are other times when on a nice straight interstate highway, most of us will allow some movement to use the rest room, grab something to eat or drink.
To move around for any length of time to play with a child, that may be pushing your luck. Again, just use common sense and think about what could go wrong. You are the parents and part of your job is to take care of your children who do not have the knowledge that you have.
