There’s a book called ‘love yourself like your life depends on it’ by Ravikant. You may find the exercises odd but they require no thought or concentration, just follow the instructions and put reminders on your phone to do them regularly.
Refusing to have the children unless it’s exactly his way is also not thinking of his kids. He would prefer not to see them then see them alone. The way he refused to see them, unless it’s on his terms, is showing he is prepared to leave them. Or at least use them to get his way.
Maybe they would prefer to sit and watch a film with hugs rather than noisy soft play with a new woman after their home life has suddenly changed. Maybe they need one on one. Maybe a quite playpark or a walk in the country would suit their mood better. What about what they want?
I could never leave a spouse this way as my children come first. Assuming no violence he he has waited for another bed to slip into rather than leave with dignity.
If the relationship was an issue he could have suggested 1) counselling
2) talking and a separation without another party involved.
Theres a chance he’ll start messing around with your feelings and head, it’s very common. Read chump lady and the surviving infidelity forum.
Also ‘not just friends’ by Glass (a book).
It wasn’t you that caused this. It’s him. You were in the same marriage. To cheat you betray yourself first.
Build a world for yourself op. What do you enjoy? Music? Books? Films? Sport? What are your values? Write them down and live by them every single day. And keep a journal about this. Mediation and yoga. Weights at Home. 10k steps. Build a daily routine and force yourself to do it. Talk to everyone. Build your world. If you start today you will feel better. It will take months but you’ll get there.