I want to clarify my position: Like GH31 said, your exW doesn't have a right to protest. For me, I self-imposed some rules on myself thinking I was upholding some higher standard. That's what I wish I hadn't done. Now I was nowhere ready to date and it wouldn't have changed my behavior, but I would have taken some pressure off myself to be a "good" person.
The other part of this is that needy people tend to lie in order to get needs met (feign availability, express they are over it, when they aren't to a romantic prospect). Doing that to another person in order to get affection/sex/etc is cruel. You got to be honest about where you're at.
And, again, you especially don't want to involve your kids.
PS: GH31 - I had my one and only 1 night stand and found it cathartic in a way. It wasn't a particularly fulfilling experience, but it helped me get past something. I haven't had a desire to do it again since.
I don't care, then I do, then I don't, then I do... la de da