She made her decision, let her live with it. You have a right to be upset, but I wouldn't throw this stick in the spokes of your friendship, because this is *her* parenting issue, not yours, and it's likely that a full-blown conversation about it isn't going to resolve anything.
Does it help her child to have his whims met? Probably not.Will he learn that sometimes, there's just stuff that we *have* to do and we have to stick it out? No. So, in short, not a character-building moment here for him.
On the other hand, while you can't control what she does with her son, you can decide if/when you want to make plans in tandem with her, now knowing what you know.
I'd encourage your son to find some common ground with some of the other kids, and not bring up the other boy unless he asks. Privately, let the counselors know that your son might need them to bridge the gap a little and get him involved with a couple other kids.
Then, on your end, do this: don't schedule another camp with this child. Playdates? Find a place to meet halfway and then confirm before setting out to meet them.
She's being wishy-washy on her limits with her son, but you don't have to be make yourself subject to his whims and her permissiveness. Make your own plans accordingly, and if the other child's 'whims' make it easy to include him, fine. If not, too bad-- they can get together another time.:)