Sorry that was a bit blunt as I had baby on one arm!!
You will get great support here, so keep calm.
Now isn't the time to make any decisions at all - there's no rush, your feelings will change from hour to hour. Don't even think about what you might want to happen - just don't stress about it at all yet. Plenty of time.
What IS time dependent is a. getting evidence and b. securing assets. I know all that sounds terribly dramatic and aggressive but you MUST DO THIS - even if you are already thinking that you can sort it out. The point is that this will have shown you that no, you don't know the person he is, and you DON'T know - as you might have once thought you did - what he might do to shaft you. So you move to PREVENT any possibility of him shafting you first, THEN you think/talk. (Secondly, making swift moves to secure finances especially is a VERY effective way to show him that you will be no pushover, whether it comes to wanting him out or wanting to know all. And that's no bad thing...)
So - great that you are the breadwinner. Secure the joint account so that he can do nothing. Get some of his possessions together so that if he comes home, you can have a bag in the porch and can tell him to fuck off for a week without him having to come in - this means you don't have to face him or talk until YOU want to.
So - evidence. Don't sweat too much if you can't get back in to email. YOU KNOW, and that's the important thing. You need no more proof, and if he tries to go down any minimising/denying route, you just refuse to talk - 'right, I can see you've made the decision, by lying, to end our marriage - bye.'
Secondly, after the bank account, try and get details of his finances, pension etc.
And no - it's not your fault. Partners with small babies tend to have little or no sex. They BOTH miss it. Good partners go through that together, both focused on the babies, then work to get it back. Selfish shitheads, however...