Kaylee honey I am so very sorry you are going through this. This type of betrayal is so enormously painful that some people consider it more painful then grieving a death of a child. And it is compounded tremendously by the gaslighting.
You don't need any more proof. There is nothing that will force your H to be honest. He may even be deluded enough to pass a polygraph, so don't bother with that. You know he cheated and you know he's lying. I will share my story as a cautionary tale.
I became suspicious in 2011 and started doing some digging. Eventually I asked my H to bring home his cell phone records from work. He brought home the bill. (Grrrr) I was able, however, to hack in, change the password and see the text and cell records for 2 years. There, in black and white were the numerous calls and texts back and forth for two years. He swore on all that was sacred that it was "only" a mentoring relationship that became inappropriately frequent. I called her and she confirmed this. I lost it, threw him out, told my parents and our kids that we were divorcing. He apologized to them all, promised me "anything", went to IC, bought marriage CDs, became more attentive, etc. I let him come back.
But it was all a lie. Fortunately he had immediately ended the A, but he lied to his IC and avoided looking into his deeper (very deep) issues. I still did not feel safe and kept waiting for the other shoe to drop.
The other shoe dropped in September 2012. I got an anonymous letter that claimed that his "EA" was actually a PA and that he had started up with someone new. (That part was actually untrue and verified with a polygraph). I called the OW again and this time she confessed.
When I got home I told my H I had spoken to her and I wanted HIM to tell me the truth. He said he thought I was bluffing. I told him it didn't matter because I was leaving him anyway but it was time that he started treating me with respect. And finally, FINALLY, he started being honest. I got the truth about stuff he had lied about for decades. (Btw it was an almost 4 year PA, without a love connection)
And that was the beginning. He had to stop lying to me, but more importantly, to himself. He had to face the shame of who he had become before he could start to change. It is a long road, he has some real childhood trauma to face and he still fights facing that, but he knows that he must for himself and that I won't accept superficial solutions any longer.
Perhaps your H is capable of this, perhaps he is not. But you will never be safe with him until he can be truly, deeply honest with himself and with you.
My advice? Just refuse to engage him beyond child and financial discussions until he is ready to be fully open and transparent. If he wants to be with the OW let him. What have you lost? Disengage as much as possible. What he is currently putting you through is abusive. If he is back in the house ask him to leave. You will find peace more quickly without him there.
And please, don't apologize for wordy posts or for "whining"! We all get it. Please lean on us. I SO wish I had found SI after my first Dday in 2011. I would be so much further ahead by now.
Feel free to send me a private message if you would like. I'm not on here all the time anymore. My R, while having it's ups and downs, is going very well, and my H is a "new man". Willing to work on his issues, totally honest (for the first time in the 30 years I've known him) loving, open, attentive, giving. But if he can't continue down this path I will walk away. Never again will I writhe on the floor in that kind of pain.
My heart goes out to you.