Is this cheating? Forgiving a cheater? Did it work out?

Found out my husband linked up with an sex partner on Snapchat and had her pics from when they used to have sex saved on there from back in 2017(before we met). He sent her a flirty video of him and she never responded. He deleted her. Fast forward 7 months, he added her on Snapchat again. Pics and videos still on there from 2017. He never sent her anything. She didn’t send him anything. He just added. But I found it, and that’s how he was caught.

All I do is work my fucking ass off to provide for our family (I took no time off after having 3 babies. I was back to work within ONE week after giving birth.). Mind you, I was 2 months postpartum when this first incident happened.

Yeah our relationship has been rocky for so long, but the amount of times he looked me in the eye and fucking promised to the gods he would never do something like that, and the fact I trusted him with all of my soul and being, is beyond me. I’m absolutely rocked.

The problem is we have 3 babies under 5 years old together, and I can’t kick him out. I need his help with them. And if he gets kicked out, he would have to move to another state where his family is and who knows when he would see the babies and their lives will be turned upside down because they are so young and wouldn’t understand where their dad went.

So basically I’m sucking it up and taking him back strictly for the kids sake. I will avoid him and I’m just waiting for an opportunity to revenge emotional cheat myself, POSSIBLY 🤷🏽‍♀️. He can go fuck himself for all I care, but my babies love him and now my babies come first before me

Anyways, I think he cheated. Would you consider this emotional cheating? what do you think of this situation?

I’m lost and need advice and help.

And no, I do not have family or friends around to help me if I kicked him out. And those old sexy photos of her are burned into my mind. His defense is “those pictures are from before you!!” Yeah my response, “But you still had them there to look at when you added her, dumbass”. He’s a piece of shit