Your post makes me so mad.
What a horrible thing to do or not do for your kids.
At the end of the day you have done everything you could to prevent this from happening & you have to tell yourself that.
You were also right to explain this to the children & prove it.
You can't control what goes on when he has contact with the kids.
The children will quickly learn who is reliable & who is not, doesn't make it any easier I know.