H said the following to our son, although he was really talking to me (and my son was not paying attention): "Maybe I should just home school you buddy. It may be the only way for me to see you since mommy only wants to let me see you one day a week."
This kind of comment and talk in front of your kids is completely unacceptable. Please set a boundary with him that you all will not bad mouth each other in front of them.
I could go on for a while on the effects it has but you seem sharp enough to realize this is not in the best interest of their emotional well being.