What you describe in your STBX is from everything I've read here and elsewhere an incredibly normal reaction by a selfish person.
You mention that things are progressing slowly. In some cases people will add conditions to a parenting agreement like "no overnights by strangers" and when / if / how a new person can be introduced. I expect that in your case that the other party isn't rational enough to think of that. I presume you have and expect to continue to have sole custody? That does affect things and reduces his rights wrt to the children I believe. Since my own kids are adults I've not paid too much attention.
If it becomes a problem, actual real legal advice may be required but if you look past the spew and anger and him trying to maintain ownership of you it is something you probably need to take seriously.
I'm glad that you've found a bit of a flutter in a new friend. No telling where that may go. I've had more than a few false starts of my own. All of which made me feel good about myself discovering that these charming, interesting ladies find me worth some of their time.
Glad to see you (((Cherry!)))
On BD H52, W50 T27, M26 S21, D23 BD-9-Mar-16 D-15-Jan-18 Final-19-Apr-18 I am a storyteller. The story may do you no good. But a story is never for the listener. It is always for the one who tells