Docking station

Anyone have ideas on what the best docking station I should use to play my ally x on my big tv if possible? And I’m not looking for people to be nasty and hateful towards me I’m new to the hand held world and my switch runs great on my large tv but this ally x with the dock I have is quite sluggish. Like for instance the other day I tried playing an emulator and playing super Mario world and on the ally it was buttery smooth but when connected to the tv there’s a massive multi second delay from the input and the characters movements were way slowed down any help is greatly appreciated.