Hi Tears,
When the MLC wants to get back together they call the process "piecing" on the board. You need to look up threads about "piecing" as that's where the reconnection process is most talked about.

One thing that sticks out in your post for me is the fact that the OW's kids know him well enough to send him Father's Day cards! Wow, how long has he been with her that her kids think of him that way? How sad that is for the kids as it's not their fault that their mother hooked up with a married man! I haven't gotten close to the piecing stage myself so I don't know much about it but I can tell you it's going to be a hard process as he will need to be VERY open with you about what he is doing and where he is going, etc. AND he will need to be open and honest about it.

Stay strong, set boundaries, be ready for him to slide back a bit now and again. Read up on how to reconnect. It will be hard as you must feel such betrayal but remember the OW is just a symptom of the MLC. She's probably someone he never would have noticed before he started the MLC. Good luck and let us know how things go!