Probably the router, but more likely the phone service. The TV probably makes the situation worse. Some years ago, I faced this with adding a smart tv to the house. With gaming and multiple users and the tv, the internet connection we had was stressed out. It seemed to confuse the router. I had to change the wifi name so the tv couldn't find it. That helped some. Changing to a different router helped but not completely. The phone company finally agreed that they had a problem. They decided to throttle the dsl speed instead of fixing their lines. Changing to cable instead of dsl was what finally solved things.

I still have the same original router in a different house and it has been pretty good for the past three years in a much lighter environment. I will need to change it finally as it is unreliable again, but it's also over 10 years old.