Advice please! Husband lying while I’m pregnant

I’ll try to make this as short as possible ... quick back story my husband and i recently got married back in May, I’m currently 40 weeks pregnant.. back in oct around the time that I found out I was pregnant I noticed he was acting a bit strange (had his phone with him at all times, even when he got up in the middle of the night to use the bathroom he would take his phone) but I didn’t think much of it because I trusted him ... he doesn’t make any post of our relationship on social media which is fine with me but anyways ,moving forward to a few weeks ago he was showing me a picture on his phone and a Snapchat came in and he quickly took his phone back which I found weird.. then I noticed that whenever he is using that app if I get too close to him he’ll exit the app right away or turn around so I won’t see his phone ... I started to have a odd feeling about it so I decided to check it out for my self, mind you he always looks through my phone, reads my messages which I don’t mind since I’m not hiding anything so I figured I was just being paranoid and I wouldn’t find anything .... well to my surprise I found out he’s been talking to his ex.... and what hurt the most was that he denied being married when she asked .. I guess she heard that he was now married and asked about it and he denied it .. also seems like he was the one who reached out to her because she told him that he can message her whenever and she’ll reply .. she also asked if I was “okay with them talking “ he said I was ... mind you I had no idea.. yesterday I broke down and couldn’t keep it to myself anymore and brought it up. At first he denied it, then he tried to pin it on her and later said he had to keep in contact because when they were together two years ago she was depressed .. he didn’t even apologize and just said it wasn’t cheating because they never met up ... honestly I don’t want to see him right now and I don’t want him near me, I don’t want him in the delivery room with me but I also don’t want to be that person.. I’m thinking of taking some time and going to my parents house after the delivery for a few weeks but idk ... any advice ? (Sorry for the long post ).