He wants to bring her to your house??? What nerve!!!!! Wow, my husband never would have done that. I would have verbally cut them to shreds (and maybe even take a carton of eggs and lobbed them at her!). Grrrrrr....
But of course, they would have said I was nuts, or childish too, used this against me some way in court, my husband would have said, "Now you can see why I wanted to divorce her," etc...
Really, even if you have daydreams of all the mean things you'd like to do, it's always better to take the "high road." You want to be the better person. This doesn't mean you have to be stepped on or have to act like she's part of the family. You have a right not to have her in your home and you can tell your husband in a cordial manner that you don't approve of the relationship and don't want her in your home, around you, phone calls from her... nothing! You are entitled to your privacy.
Unfortunately, you probably can't stop her from being around your kids when he has them. You could look into a legal separation that would give you more control, but that's about it. Hopefully he won't want to have them over often. Although sometimes, that little bit of reality can make a difference. One of my previous neighbors was a 38-year-old divorced dad (two boys) who married a 21 or 22-year-old single girl on the block (she was living with her parents). I heard after a few years that marriage had a lot of difficulties because this woman found the kids overwhelming (even at 22 she was not ready to be a mom to two pre-adolescent boys! She had more growing up to do...). I think they eventually divorced.
Truly, what you need to do is quit worrying about your husband and just take care of yourself and the kids. Keep GALING!!!! Detach and start having a life. What are you doing for yourself???? Are you working out? You need those endorphins. Are you going out? Have you bought yourself a new outfit? (something super attractive!!!).
There is no arriving, ever. It is all a continual becoming.