Similar story here.....

Several items on my in house network are direct to the cable modem. Wireless router is just one of the things that's also plugged in as a branch and used just for the wireless node it provides. There's also a hardware firewall that also acts like a switch, into which all the wired computers and some of the other devices are connected..... computers, alarm, additional remote switches, phone booster gizmo, etc....

When I switched from one provider to another, I had to run the TV aux devices direct as well. They ran fine on wireless with the other provider but not the new one.....and no amount of support would get it done.... like you found out...one support guy blamed the other one's device and vice versa..... so a cable direct to the modem, and it was working like a champ.

You can find my music at:
www.herbhartley.com
Add nothing that adds nothing to the music.
You can make excuses or you can make progress but not both.

The magic you are looking for is in the work you are avoiding.