Keeping personal emotion out of it is the best, really difficult, but best. It is a completely reasonable request for her not to bring OM to house. I had the same request for years, actually. Now, I let her in my house with nobody home the other day to drop something off...... I would actually like to suggest something, and this is just from years of experience in this "field"..... I might take out the "ever again". This is something you may not be able to wrap your head around at this stage, it's something people never wrap their head around, and it took me years to do so myself....and please, I apologize if my timing isn't right with this...... they might get serious one day. They might get married one day. They might be involved in your kids lives. and you might be letting him come by to drop off your kids, or a project for your kids like OWW wife did the other day. So for now, yeah, completely understandable, ask for her not to bring him by the house. But maybe leave off the "ever" again.
It's a process to accept the OP. my ex put OW in my daughters life when she was a baby, and I believe before he dropped the bomb. I did say my daughter was never to be left alone with her until I OK'd it (probably didn't listen) and I asked that he lets me know when she moved in and when they get engaged. He complied. I also offered the same respect that when I date someone, I will let him know when I plan on introducing her to him. I only introduced one, he knew about it, was fine with it (considering it was 8 years down the pipes) and he thanked me for doing so.
Again, I apologize if this is too much to wrap your head around right now. This is not something I encourage you to do right now or even in the near future. You will know when it is needed or right. Sometimes it never is. But it's also a possibility. That's why I say to leave off the "NEVER again".