It doesn't affect anything in the house, not even if my wife is watching Netflix but it lags me out of any session in GTA and then I'm in my own lobby.
What I do is just disconnect the cable to my router/modem box for 5 seconds. I sell IE cars a lot in solo, public lobbies.
I have most businesses because I get bored and switch around. I only grind solo, just went over 50Mil and now at almost 51 mil after selling my bunker stock and doing some Simeon double $$$ missions. I don't know if my advice will help or not.