To the OP, as a foster family, we can totally sympathize with the situation. Our household size is always in flux, making plans for travel all kinds of fun!
We lead a local support group for foster/adoptive families. Whenever we plan a camping trip, we open it up to include families from our group as well. If we plan to camp over a long weekend up to a week, we will get a group site. Having multiple families camp with us really offsets the costs of the site and makes it a reasonable cost for everyone. Plus, the group sites we stay in are away from the main campground, so our kids can feel comfortable being themselves without judgement. For shorter weekend trips, our group will dry camp in the woods. We "circle the wagons" so we can create a common area in the middle, making watching all the kids so much easier.
I would recommend that you find other foster families in your area that you can go camping with. Camping is so much more enjoyable when you can share it with people who totally understand all that comes with fostering.