Wow, a triad if issues. I'd have to ask what sort of relationship this is? An open marriage? She dates others? What do you do? Maybe you need to find a girlfriend to spend time with as she does?
Never would I let someone put ultimatums on my relationship, that's a deal breaker. Previous marriage issues but all is well as long as she can see him? wouldn't every relationship be splendid if you could stay married and date others to satisfy your needs?
It sounds like your in a serious emotional wreck trying to maintain a relationship by letting her date him. And when you ask her to stop she threatens you.
To me this only says the relationship is over and she is staying with you for financial support and the kids. Regardless of what she says.
I haven't heard that the 3 of you do anything together, so it seems as if she is doing your buddy and having her cake too. What you need to do is get your act together and figure out what the hell it is you want, build up your self confidence and stop letting her manipulate you.
Just my 2 cents without looking too deep into it.