I understand how hard it is. For me, I found it worked much better to keep my dating life and my mom life separate. They don't have to like who I date, and who I date doesn't have to like my kids. It would be nice if everyone all got along and had fun times together, but I don't think any of us is ready for that 'family situation' yet. So, I spend time doing things with my kids, and I spend time doing things without them. (BTW, everyone has met, but the guy I'm dating wants to date me, not my kids. And, my kids have no interest in another "man" in their life, they already have a dad.) It works for me.
I guess I'm wondering why you spend every other weekend with his kids. And, are you feeling guilty about your kids because of it? I see no reason to force my date on my kids, or force my kids on my date. This guy isn't looking for someone to be a mom to his kids, is he?
L