Separated and Dealing with Ex's Dating

Been separated for several months and found out that my spouse is dating someone and has introduced them to mutual friends. I'm not sure how to work through how this feels... We still do a lot of things together because we have children and we're friends, and I hate knowing that now I can't be in certain places because the new "partner" might be there. I also hate the feeling of being the last to know.

I also have come to the realization in recent months that I want to reconcile. Currently my spouse does not feel the same way, although they did not long ago and it feels like a pretty fluid thing and we've only recently stopped being intimate because of this new partner. My spouse is nothing if not fickle, so part of me feels like I should just not make a big deal and just hope this relationship fizzles out. We have children together and I just hope that he doesn't involve them. I'm just trying not to think about this as the end of the world, but sometimes it really does feel like it, and it hurts to know that there's this stranger who's slowly replacing me in every aspect of my life.