I think his having been cheated by the kids' mother was not caused by you in any way (right?), so that he would demand that you not spend your time a certain way due to that is bizarre, irrational, and unreasonable - you need to assert your right to spend your time the way you want to. And where would you draw the line if he makes you responsible for actions that were not even yours? Say, what if his ex tried to poison him by putting a substance into his drink - would you now not be allowed to have drinks in your own house that you bought for your own money?..

The TV thing - if they can use headphones so that you would not get a headache, would that solve the probem with the TV?

Where does he live and why cannot he have the kids spend the time with him at his place and watch his TV?