I feel like what they are doing is kind of cheating because they have feelings for each other (they even admitted to it) and are hanging out despite her being in a relationship with you. You don't have to do sexual things with a person who isn't your partner (or boyfriend/girlfriend) for it to be cheating. It seems like emotional cheating to me.
This must be really hard for you because you still love her, but you also notice that she seems happier with someone else and that it is helping her mental health. Like someone else suggested, I think it would be good to do couple's therapy. You may even need to ask her if she is still interested in being with you any more because this type of cheating could definitely escalate into something more, though they'd probably do this part secretly.
There is unfortunately a chance that she will leave you for him so just be prepared in case that happens. Reach out to loved ones if it helps and do things you enjoy and spend lots of time with your children. In the mean time, it is very important that you find out if she still wants to be with you to save you from getting even more hurt further down the road.
If she says she still wants to be with you, but also wants to spend time with this other man she also has feeling for, ask her if she would like it if you started dating or spending time with someone else that you also had feelings for. I don't think she would like you doing that and if she doesn't have a problem with that, then maybe she doesn't even value the good thing she already has that much.
If you can't at least get her to go to couple's counselling with you, it would be good if you could see someone by yourself, because while what she is doing may be helping her with her mental health, it's probably making yours/going to make yours' a lot worse.