Barb makes some excellent points.
My kids go to sleepover camps, and my family did growing up. I also went to girl scout camps as a child and my kids have gone to scouting camps too.
I think getting it subsidized would be the way to go - if it were me. The big sleep away camp my kids do is a Christian based camp - kids do not have to be Christian to go, nor go to church, it's just who it is run by - they are willing to negotiate camp fees I believe. That's the whole reason they do the camp - so it's inclusive. I know a lot of kids are from foster care, etc.
I think that's the same for sports camps around here also. They are not necessarily sleepover camps - but I know they support all income levels.
As for working there too - I have not run into this with my kids experiences. Seems to me that might have been the case when I went to camp - I don't remember the child mingling with the rest very much, but it would depend on the child. I agree with Barb that part of the experience for kids is to be on their own and gain independence. However, i'm sure it happens and works for some families.
It would help to know what area in particular you are looking at, so that moms in that area could respond with actual camp suggestions to give you.
**My husband has volunteered at scouting camps now that I think of it. They were more for long weekends, but that was a simple enough process - he just had to have his security checks done. With scouting, I think there are always some parent volunteers. He was on kitchen duty (preparing bonfires, clean up, making breakfast, etc.). On the plus side, he is still good friends with the dad that he met while doing that.