to trust again or just leave

me and my husband have been together almost 5 years and married almost 3. well he took a job out of state a few months back and I caught him messaging other wemon. it was a total accident I got on his email for a confirmation number to our car payment and seen what he had been doing while out of state working. now none of the conversations actrully sounded like they met up it was all just sexual talking and pictures. + he made a Craigslist add 😡. We worked through it and he quit his job and came home and things have been great but I constantly battle myself daily on how to trust him again. I have his passwords and I go on his shit daily as well and I find nothing every time... but I'm sure he's smart enough to just delete his shit this time. We have a 3 year old and a 4 month old together and I honestly think that's what's holding me back most. but I'm so undecided on if I want to pack up and leave or stay and maybe 1 day I'll trust him again and not look back on everything that happened. I need some advice please.