If you haven't thought more about it, I highly suggest getting the kids, if they will accept it, to talk to a good therapist. Ask around for recommendations and shop carefully. In my mind, you don't want your kids to have to deal with this later in life, a la MLC for themselves.
For kids, it was once explained to me that their stability comes from their parents - their relationship, and their home. It's an important part of their life. To interrupt that is devastating and difficult in many ways. Many of those ways are not seen until much later. The MLCr, if like mine, think that everything is fine, everyone does it, and the kids will be fine. The lies we tell ourselves.
In my case, pushed for my kids to go to a counselor. My ex fought it for a long time. Then she decided the kids needed to go (at her lawyers insistence) and forced them to go. I don't recommend forcing it. Was it helpful? I think it was good at sowing some seeds, but I think the forcing them to go was the wrong way to go. They didn't want to be there. My son won't. My daughter went several times. But the story isn't over for them
I took the approach that I couldn't stop what ex was doing. I don't talk badly about her if it comes up, but I see the anger in my son. He'll talk to her husband and act like things are fine. But my instinct is that he is not. My daughter is also not fine. She chooses to take her anger out differently and give her as much space and time as I can. Both of them.
I can't change what has happened or the choices that were made. I can only be there for them and be stable.
As for dating, I highly recommend you not introduce the kids to anyone new for a very long time. There are a host of reasons, but one of those is that you wouldn't want them getting attached to somebody that may not work out. It might seem like they were "left" again. Make sense?
Peace, AJ
"Our lives begin to end the day we become silent about things that matter" MLK Put the glass down... "Yesterday I was clever so I wanted to change the world Today I am wise, so I am changing myself."