Oh OP - this is all so upsetting to read.
Many years ago I found out two years into a relationship that my DP may have cheated on me. I confronted him and he denied everything, but then slowly admitted to more as I continued to prove him. He acted remorseful, did all the apologising, did the minimalising and cried lots of tears but something in me just knew he wasn't being completely truthful.
I obtained a copy of his phone bill (in a sneaky, probably illegal way) and found the woman in questions mobile number everywhere. I contacted her and arranged to meet her.
I gave my DP one last chance to tell me the truth or it was over but he promised me that all he's done was kiss her once, it had been s mistake and he'd never do it again.
I met up with the OW and it turns out things were far, far worse than I had imagined and they'd actually been having an affair for months. It broke my heart to hear it but God I'm so glad I found out the truth.
Life is absolutely too short to spend your life with someone who can cheat on you, lie to you, deceive you, manipulate you etc. You deserve so much more.
Your DH doesn't deserve anything and in your situation (as I once was though without children) I would ABSOLUTELY do whatever it takes to find out the truth.
I could never have stayed with my DP without knowing the truth. I can't imagine how painful it would have been every day to always have that doubt, to always be internally questioning whether I believed what he said and whether I could ever trust him.
You deserve to know the truth and he absolutely doesn't deserve to get away with anything.