Forgiving and staying is as hard as splitting up IMO
Only you can decide OP
You need to realise that unless you decide and put your foot up her ass (not literally of course) you will suffer and eventually your kids will pick up on it and they will.. trust me, they will notice something is up.
Force her hand. Either she wants you or she doesn't. ATM she is having her cake and eating it no matter whether she is happy with her life or not..she has no right to make YOU unhappy, in trying to find whatever she is looking for to make herself happy.
The greener grass on the other side of the fence is actually astro turf IMVHO.
What i count myself as with my DP, yeah, sure, there are better looking guys out there, probably with bigger cocks, nicer cars, more money, their own house, whatever, maybe someone who will say "I love you" more often, or who will be like a porn star in bed, who will notice when i have my hair done .. why would i want someone like that? They IMO wouldn't be a patch on my DP pain in the arse that he is sometimes, they wouldn't tell me they loved me even though i smell like baby sick, am up to my armpits in nappies, not notice i have had my hair done but say nothing when i haven't brushed it
I wouldn't swap that for the world.
You give up such things when you commit to someone.
I know you don't want us to judge her but she is taking you for a prick mate, a soft touch.
If she gave a fig, or was made of anything, she would have come to you BEFORE the affair started and would have told you, "I am not happy, this is what i feel is missing/could be improved" Then you could think about it, and come back with an answer, or have a discussion about BOTH of your needs ect.. and sort something out between you.
Not happy? Doesn't know what she wants? FGS you are a man not a mind reader.
She should have told you and given you a chance to put things right or at least make them more bearable.
Hmph i fucking HATE cheaters. Lowlifes.