That's tricky and frustrating.
Remind me how many kids you guys have, and ages?
I'm guessing that when you gave this background:
I explained to them that uBPDH has certain emotional issues which I and my children are struggling with and I am happy to communicate and cooperate with them exclusively.
it was documented (like email, etc)?
I even met with the principal every couple of weeks to monitor anything that might have come up.
That also seems like a good thing to point back to -- and I'm sure those meetings are documented as well.
How did you find out that H "did his own thing" in getting in touch with the school? Did the school tell you, or the kids, or...?
...
I know it's a lot of questions. Just getting a better feel for the moving parts.
First gut feeling, overall I'm wondering if "putting the school's work back on them" might be a way to go -- to assertively remind staff that "hey... per my email on Day/Date/Time, I am the parent-of-contact for any issues with our kids. If there is an issue with the kids' dad contacting you, please remember to work with me, not him. Thank you for adhering to this arrangement going forward."
or something more... IDK, blunt.
...
One last question:
(uBPDH wasn't too happy, but was relieved to be absolved of involvement.)
any documentation of his "agreement" that you are the "parent-of-contact"?