why are people talking about confronting the woman in this? its her OH who is the serial offender here. this isn't his first affair.
OP you know already in your heart of hearts that you have all the evidence you need. late night texts sometimes twice or more in an evening that he then deletes when he doesn't delete anyone elses messages. and you only found them because you overheard him telling your son his password so you could get into the phone.
absolutely do not confront her. he is the one in the relationship with you and not her. confronting her gives him time to get his ducks in a row. you could confront her, she contacts him then when you get home he will do the
"I didn't want any of this. she has been pestering me. I didn't encourage her I have been trying to put her off. poor me, I am the victim in all of this of her unwanted attention. I deleted the texts to save you any hurt or embarrassment"
I am sorry but you have to take control of this situation and do it really quickly as I said in previous posts. you can only hold onto his phone for so long. so use the time wisely to get everything financial copied to you or password protected by changing passwords.
of course the kids will be upset. but honestly don't keep letting yourself be this knobs doormat. doing all the shit stuff for him whilst some other woman gets all the goodies.
for goodness sake ignore those people telling you to meet her or to take her phone or any of these other suggestions. he will dump her to save himself like a shot - men like this always do. he has form for it - making out that you are the mad one so why not make the OW out to be mad?
OP its happening, it really is and you need to very quickly deal with it. please don't do the staying for the sake of the kids thing. that will just destroy your self confidence and is only ever going to end even more badly.
I feel so sorry for you having to confront this but you do have to. speaking to her, following him, bugging him all this nonsense its just a diversion from dealing with the hard facts.