There is no problem having benign relationships/friendships with exes.
When they send messages clearly of a tone that is improper, inappropriate and disrespectful, then it's NOT helpful to your relationship. to continue on with conversations like this KNOWING they are hurting your DW/DH is WRONG. It is disloyal, it is unfair and it is betrayal.
My X had no right to stop me talking to my ExH, I know that now. He banned me from contact with all kinds of people. But that is because he was abusive, a fact I didn't know at the time. I needed to be more confident at the time and know that what I was doing wasn't wrong.
If I had have been having conversations of the kind you describe here OP, then tbh I'd understand my P's upset and if I didn't respect him enough to either tone it right down or reconsider my contact with that person, then there ought to have been consequences.
This DH knows what he's doing is wrong on many levels, I think he IS lying about the Flight to Egypt thing. I am sure his Ex is in full possession of her faculties too.
It is not controlling to ask someone to stop badmouthing you to a hostile Ex.
If this Ex were fully supportive of your H's new life, really happy for him when he proposed to you, delighted at your marriage, at ease in your company etc then fine, you wouldn't have a problem either.
My experience so far I think IS pertinent, even if certain new blow-in posters don't quite get it, in that I've been controlled, told who I'm allowed to speak to, without reason. I also stood up to him and ultimately chose my Friend over X in the end, once I realised what he was actually trying to do. You are not that person OP, you are not controlling him, you are merely asking for your deserved respect and consideration.
I'm saying that you DO have reason here to speak to your DH and ask him to tone it down and discuss your problems between you, not with an ex who has some kind of axe to grind/ulterior motive.