I am sure this is an emotional reaction to the statement your friend made, but personally, I'd be pissed. There is no way I could go to her house, all happy-go-lucky, and feel comfortable at all, knowing that my childrens' behavior is being scrutinized to the extent that if they aren't perfect angels, they are not welcome.
Kids are kids, not robots. We cannot predict how they will behave 100% of the time. If their behavior was never an issue before, I can't fathom why your friend would make such a comment based one visit. If your kids frequently have behavior problems at the friend's house, then I could understand, but your friend stated that they are typically well behaved. So I don't get it. I'd have a serious issue with going back there to stay.
As I said, I know this may not be the "high road" approach to your situation, but I am speaking honestly. If it were me, I'd be really offended. I would tell my friend that we are not coming. If asked why, I'd explain that it's because I can't guarantee that my kids will be perfect angels 100% of the time and I don't want to be uncomfortable worrying that we might be expected to leave if the kids don't behave perfectly. I'd welcome them to come to my home anytime, but tell her that I won't be staying at her home.
I know this might damage the friendship, but for me, the damage has already been done, when the "friend" made the comment about the kids. I'm not saying that kids should be allowed to run amuck in someone else's home (or their own for that matter), but it doesn't sound like your's did. It sounds like they're normal kids.