For your SNES gaming you need a Hyperkin SuperRetron HD, Gamerz Tek 16-bit HD, or a Retro-bit Super Retro Trio HD. Either one of these would allow you to use the original SNES game pad. That is unless you are experiencing some sort of latency issues between the TV and the console, incompatibility maybe?
For multiplayer gaming with your children, I would suggest the Nintendo DSi "Bomberman." It is always fun to blow someone up. Get that competitive spirit pumping. Also Animal Crossing, my daughter an I have enjoyed that for years. Mario Kart racing is another one of those competitive games.
I like dedicated gaming systems for gaming. I recommend DSi or 3DS. On the 3DS the monster Hunter game could be a winner.