Best advice given to me and worked for me:
Treat coparenting the same as a business. Everyone should pay what is due, this is calculated by a third party and is (generally) fair and impartial. When e-mailing, word it as you would a business letter, and try to remove all emotion, and reiterate every point with "in the best interest of the children".
Ignore abusive text messages. Do not respond. Perhaps inform him that you are keeping a record of all correspondence in case you need it at a later date, and communicate via a new e-mail address set up purely for communication with him. That way you open them at your leisure.
New partner is F all to do with him. He will just have to suck it up - not one rule for him and another for you. You deserve to be happy too.
Keep a diary, of everything, no matter how trivial it may seem.
This will help you should things ever get that nasty that you end up going to court.
The law recognises controlling and coercive abuse as domestic abuse, if you contact your local DV charity they may be able to offer help - and I fully recommend the "freedom programme" - it opened my eyes big time.
I hope any of this helps - and sending hugs xx