Hi fightingback and thanks for the congratulations.
I'd suggest that you work out an agreement between you and then have an attorney help you make it formal and binding. You can usually find a family-friendly attorney to serve as a mediator for a process like this.
I can certainly understand her hesitation to spend money on it -- but it is MUCH better to spend a few hundred dollars now than it is to end up disagreeing ... and then spending many thousands of dollars on legal fees afterwards.
Not only does it save money, but it also protects your kids even further than you already have. Since your kids do not have the full protections that the law gives to children of heterosexual marriages (like the right to see both of their parents, just as one major example), you need to protect your kids with other agreements so that even if one of you is not able to make her wishes known, they can still be implemented.
There are lots of things that you'll want to think about as time goes on, but two things are particularly important right away. Those are a schedule -- for weekdays, weekends, holidays, birthdays, and all the other days of the year. The other thing you really need is an agreement on how you'll both financially support your kids during the separation. If you have those things in place, you're on much firmer ground.
I'd also suggest that even if she doesn't want to use an attorney, you may want to consult one. This is not to gain power over her, but rather to understand how both of you can best protect your children during a time of separation.
I take it that your WS has proven uninterested in ending her affair? I'm really sorry about that. It can be tough to turn the ship sometimes. My best advice is to make your house and home into the safest, coziest nest for you and your kids that you possibly can. It's so important that you build a center of peace in your life, and building it in your home is an excellent first step.
Please feel free to e-mail me if you'd like more help -- I don't log into this board all that often and I'm likely to miss posts way too much. Good luck to you!