@ChuckleBuckles I agree, repeated infidelity is a form of abuse. Unfortunately I was a bit taken in by the ‘I may have a sexual addiction’ or whatever. It’s much clearer when we see things through their effect on us, like the OP and her family. Whatever her DH is spouting, he is harming his family repeatedly. In a huge way. Lying to your partner and family is huge. Lying that there is a family, as there is not as he has actually left the family, and worse of all he is pretending he hasn’t. He’s not being a father, or a husband. Fathers and husbands are people that you can trust. This is abusive.
Also, once someone starts lying and betraying they family, repeatedly, like abuse, I think it tends to get worse. My Ex starting to shout more at me and the kids, which I later realize was the start of serious verbal abuse. I now believe that this was the result of further trashing us as a family, starting with the infidelities. It was unconscious. However if you are neglecting your kids and wife, by cheating, you are getting used to not respecting them as people. You are getting used to feeling that you are better than them, because you can cheat and lie, but you expect them not to. Your brain is starting to devalue your wife and kids, and things that a normal family want such as you being attentive, noticing their problems as they grow, being there for them, diminish as your selfish excitement for sex elsewhere takes over.
That is why many people feel that something is going on, before they have proof. Emotional distance is a cruelty in itself. Maybe the odd comment about being overweight to the wife. Or lack of care that the older child is having difficulties with friendships. It all builds over time. And as the infidelity is repeated and carries on, the excuses for doing it are projected outside, usually onto the wife and kids. Wife is too boring, doesn’t want sex enough. Kids are too needy, I work all the time don’t I get anything for me? Etc. This blaming is abusive.
In my case it ended with me being screamed at for asking DH to come on a family day out, because apparently that was an awful thing to ask of him. He’d been working so hard, that spending time with the people who really loved him was taken as a threat to his entitlement to just do whatever the hell he wanted. Which was to have sex with any younger woman he could find. He screamed so much that I felt scared, and my children were scared. We left soon after.
Unfortunately OP I do believe your relationship has now become abusive because this emotional pain you are now experiencing is not a small thing. Your attention and energy is being drained by your pain and your children and you need to bring that attention back to yourselves.