You say the mortgage is in your name only but is the house also is just your name or is it joint names?
Personally I think you should go to the police with the text messages, he is verbally abusive and manipulative and you don't have to put up with that.
Make an arrangement for contact, tell him he can have the DCs every other weekend, stating next weekend from 5pm Friday until 5pm Sunday (or whatever you want) tell him that is the arrangement, if he doesn't turn up at 5pm on Friday he will not get the DCs and there will be no changing the weekends/days, it is that schedule or nothing.
Set up a new email address, give him that and tell him that is the only way you will speak to him, then change your phone number.
Make notes of everything he says and does, and collect as much evidence of his behaviour as possible.
Do you have proof of when you split and when he moved out?
You need to gather as much evidence of when things have happened, when he left, how much money he has given you, etc.
you want to make sure you have as much evidence as possible to combat the lies is fabricating.
My friend went through the same thing with her ex, when she stopped engaging him he eventually got bored and left her alone.
I hope it all works out for you.