OP, the fact that you have access to his accounts and that you are not breaking any laws by checking them does not mean you are not snooping. You are snooping because you are using that access to investigate his alleged love life
So what should OP do, go in 'blind' and just sit back?
A man leaves. Ok that's his right. But any partner who's been left would be utterly stupid not to look into his affairs if possible.
MN is so hypocritical at times. All that get your ducks in a row, find out where he and you stand financially, screenshot any important documents blah blah blah.
& If divorce obviously may be the outcome of course you'd want to find out if there were somebody else...! It affects divorce matters.
I don't blame you OP, you don't have to sit passively for anybody. It's as if you have no voice as he made his decision, moved on, and that's it. After 20 years. He may think you're controlling it doesn't mean he's right, at all. Or maybe you are controlling.
Nobody here can know. But the main thing is he's gone, and being looked after by mummy(!), so your life has changed.
Some of your behaviour at this time may not be perfect but you've had a shock. I wouldn't believe anyone who implies they'd be oh so rational in this situation. This is a 20 year relationship that's ended, not a 2 year one.
& You have 2 confused unhappy children living with you too, lest the harsh folk forget.
Take a deep breath and go get some initial legal advice. You will know where you stand and can then act accordingly.
Time is a great healer is an old cliche, but it's true. Good luck.