If you just want to list two things you did not do in parallel, you can use し:
I didn't return home, and I didn't watch TV, either.
The te-form doesn't work well for this purpose because it implies some relationship between the two actions.
家に帰らないでTVを見なかった is a rather unnatural sentence, but it would mean "I didn't watch TV without returning home." (or more literally, "Not-returning-home-and-watch-TV, I didn't do it.") Effectively, this is a rather convoluted way of saying "I watched TV only after returning home".
家に帰らなくてTVを見なかった usually means "I didn't watch TV since I didn't return home." This is an example of te-form for reason. It's better to say 家に帰らなかったのでTVを見なかった, though.
家に帰ってTVを見なかった almost certainly means "I didn't return home and watch TV". A sentence like this treats the two actions as one set. You need only one negation (ない/not), both in Japanese and in English.
Some (more natural) examples:
I didn't eat it without using chopsticks. (= I never failed to use chopsticks when I ate it.)
I couldn't go to school because the bus didn't come.