Hi Anne -
First of all, I am really sorry to hear how troubled you are. But you are really asking about two very separate situations, the only common element between them being you.
Yes, I do think it is okay for you to negotiate not inviting your husbands lover into your home as a limit, especially where there are children involved. Hopefully the two of you will come to some kind of mutually satisfying agreement/compromise on that. And good for you for standing up for your feelings.
As far as the man you are dating, you mentioned that you and your husband are "taking lovers and being honest about it", but unless I am reading your words incorrectly, it sounds like the man you are dating is being dishonest with his wife - is he completely open with her about his relationship with you? If he is being dishonest, by extension, so are you. I am a big believer in honesty, and feel that a man who would lie to his wife is a man who would also lie to you. I don't think you should take part in that dynamic.
Otherwise, you just sound a little confused about what you are looking for. Good luck to you in exploring your feelings, I hope things work out for the best for you.