What if you always pick up the child with H? Or, the emails get sent to YOU and you get the info. to H (emails requiring child info.)? Or, like has been said, get a third party to do the exchange, like another family member or close friend. The OW does not need to SEE H, just give the child to him and give info to him, and that he can get through someone else.
If he doesn't have "no contact" the chances are slim that he will be able to love you like he should. He needs to go through withdrawal of the OW drug.