I was thinking (off the top of my head) I would not put it past Verizon to mess with the other network anyway or be messed with by the other network? Have you tried disabling one network when you want to use the other?

I do not have your problem, I have Comcast and only one network but using our microwave in the kitchen blocks our internet signal (router in the room above the kitchen) and, recently, when I turn off my computer (5 feet from my husband's computer), the whole internet dies/has to be rebooted.

I would pay a bit for one of the Geeks Squad/On Call sorts of people to come out and see if they could figure it out since Verizon won't/isn't responsive?