Hmm, I can only relate my experience, so for what it's worth:
  • Forget about MMOs. There's no way you can square the time commitment with parenting.
  • Short hits are good. Games that you can save and quit at any moment will be your friends.
  • Strategy games can be played, but in stages, over many nights. You ain't gonna play a Total War game for twelve hours straight for a long time.

Hope this is helpful ...