We have been traveling fine with our kids since they were infants. Forward facing seats (like the dinette) can be used for car seats as you can use a lap only belt for infant-only, convertible, and forward-facing seats. We bought one that is rated to 60 lbs with the harness. Most are 40 lbs, but this is not enough if you are going to use it until your child is 8 and 5'7". Boosters cannot not be used with Lap Only belts. You could also use the passenger front seat if you don't have airbags. (Do any coaches have airbags?) Car seats cannot be used in sideways facing seats. So, the 3 youngest would go in the dinette seats and front passenger seats.
For the 6 year old, it depend the laws in the states you will visit. In NC, where I live, if a child is at least 4 and 40 lbs and there is no appropriate seat for a car seat, then they can ride with a lap only belt. I would recommend you google "Car seat law lap only NC" substituting your state for the NC and find your states rules. You can also stop in to your DMV or a fire station and get a copy of the law. I think AAA might have them, too. Also keep in mind that just because you can do it, doesn't mean you should. The 6 year old would be safer in a forward facing seat even if it is legal for them to sit in a lap only sideways facing seat.
I did find several sites that said that it is not permitted to put car seats in a rear facing dinette seat. Actually, they said rear facing station wagon seat. So only older kids who do not need a car seat can legally sit there.
Good luck finding places for everyone. RVing with kids is lots of fun!
Stewart, Brenda and kids
2008 Newmar Canyon Star 3410, now at a new home
2006 Roadtrek Versatile 210