What's going to happen next?

[Pogmella]

Threw H out last night. 2 weeks ago I found a love letter on his phone to OW. After a week and a half apart he agreed to come home and work on us for 1 month, NC with OW. 2 days in I found his second phone so turfed him out.

I have told him I want no direct contact he can go through a 3rd party. We have DD who is 2.

So far it's all followed a very dull script. So what should I be prepared for next?

It depends what sort of bloke he is. My ex was very angry and bitter and made everything very difficult.
Do you own or rent? whose name is the house in?
If you jointly own your home, unfortunately you cannot force him out, he is within his rights to return to the home. So, he may take legal advice and try to come back.
I would perhaps go and see a solicitor to get yourself better informed.