What would you do? (Long post but pls help)

So I been married for 3 years, have an 1yr old and a 2month old. My husband and I have always been affectionate and very sexual, but this has become less and less as time went by. After I had my son, 2 months ago, from the moment we left the hospital he kept asking for sex. Everyday, he would argue with me about it. I never gave in, i was not trying to get pregnant again. 6 weeks came by, i got an iud, have to wait 2 more weeks... all of a sudden he is ok with waiting. My intuition tells me something is up. I go looking thru his things, find nothing. I know it's wrong but before we got married i caught him sexting strangers. A one time thing that never repeated itself.....until now.

I'm using his laptop because it's the only one that's configured to the printer and i needed to print some important paperwork. Anyways I go to gmail, and his account is still open. I went looking. I looked and found he had opened an account to a dating website Dec 1... 10 days after I gave birth. There was also an email saying he closed the account. I keep looking. I find an email from Amazon, tracking a shipment to a female. Some body oils and some buttlifting pants among other things...said to be delivered this week.

I imma ask him about the dating site, he lies and claims he has no idea what it is. Then I ask him about the girl by name, and says he lend someone his account n they will pay him back. I immediately call him out and tell him how is it that u tell me about your day everyday with detail but forgot to tell me this? His reply? " -_-"

He gets home from work, he puts our daugther to sleep, while I'm feeding our 2mon old he comes in the room and says can we talk now? I say idk are u going to tell me the truth? He then finally says, that the female is his ex, one he dated before he met me, that she had added him on snapchat and they been talking for weeks...and that the gifts were because noone had given her anything for her bday and he felt bad for her.

He then says sorry and that hes a sorry excuse of a husband and that he doesnt deserve to be happy but to not take the kids away from him. That he is a good dad and it wouldn't be fair to them.

They obviously did more than just talk. I dont know what to do. If it was just me, I would have been gone already. But it's me and the kids, I have never believed in "staying together for the kids" either. I don't know what to do? Now I'm thinking of all the times he was deployed (both in the military) or when we were king distance, what has he done and just didnt get caught? What was his plan to do with her if I hadn't caught him?

What would you do?