Your kids will always know who their father is. You are dad, and there will be no question, as long as you are spending time with them. Even if it's not all the time.
In my sitch, my ex left me when our first and only baby was 6 months old. She is now 8. He brought his OW in my baby's life almost immediately. I has my daughter majority of the time, but I struggled so hard that she would see them together and figure they were mom and dad. My ex leaving me wasn't the worst. The thought of my daughter thinking of some other woman as her mother was what killed me and left me angry for years.
Good news though. He did end up marrying his affair partner. They will be married 5 years on April fool's day. While my daughter has a love for her stepmother, she knows who her mother is, who raised her, and she never, ever questioned it. I've accepted a lot, and even though I do not agree with what my ex's wife did (have an affair with a pregnant woman's husband) at this point, she is an adult in her life who loves her and I accept her as that. But I will always be my daughter's mother, nothing will ever ever change that, just as you will always be your kid's father. Nothing can change that. Be in their lives, and you have not a worry. I can tell you this from experience.
As far as the other spinning and cycling and ruminating over the same things over and over, you just need to stop repeating the same thing. Use the stop sign when those thoughts enter your head, as mentioned above. You've got to deal with the situation as it is, not as you think it should be.
