OP, I agree with so many of the pps here, he isn't that invested in making it work with you, sorry.
The asking to met up - testing her loyalty to him. She is still holding on & he is giving her enough line to keep her dangling there. Throwing her a morsel now & then to keep her hooked.
Now he knows you can access his work emails, he will stop keeping the trophy emails there & delete them/transfer them to a folder on his pc/USB/hard drive/other email account.
I had a relationship with a guy, it didn't get past a couple of kisses, but was emotionally charged. I was pregnant at the time & was feeling really lost & lonely & instead of going to dp, I let my relationship with this other guy develop.
I realised I was in too deep & being stupid, so I stopped it. My partner never found out about it.
To stop the temptation, to start focusing on my life with dh, I cut all contact with him. It was hard as he was someone who came into my place of work to service our equipment.
I deleted his emails/email address (emails that I had transferred to a disk & hid at work)/told him to do same with mine
I deleted his text/phone number/told him to do same with mine
I asked him not to come into my workplace on the days I worked.
He agreed. And I got on with my life. I thought I missed him, but I missed the 'adventure'
He did end coming into work one day, several months later (couldn't be avoided) & he sent a message through a colleague (to say something really ambiguous to me, so I knew he had to come in & when). So I took my lunch & silently thanked him for respecting me enough to do that.
I haven't heard from him since I talked to him to say it was over, this was helped by the fact that I left the company when I had my baby.
THAT is how you go no contact op. That is how I fought to correct the mistakes I had made, even though my dh didn't know, I needed to fix things in my mind.
10yrs down the line from that, we are still together & dh is all I need! I talked to him about what I needed from him & we made changes & I changed too.
I worked hard to fix what I did. I couldn't have done it if I hadn't gone NC with the other guy, because the temptation would have always been there. It could easily have developed into more.
Your dh isn't as committed to fighting for your marriage as you are, op. I'm sorry, he just isn't.