Do you mean signing in on the the same PSN ID or account? Can't be done, as soon as the second PS logs in the first one is signed out. If you mean using different PSN account IDs such as "Genie 1" and "Mrs Genie 1" there shouldn't be an issue with both being signed in at once.
There are some games that you won't be able to play each other though. Don't know about Majhong (you poor guy

) but Worms for example kicks one of the 2 PS3s on the same network teams out the game as soon as Start Game is pressed, I've read elsewhere on here it's something to do with way game uses Ports for comms etc but couldn't say and out my league there. A search would probably find the posts on that though.
As for winning, just try and give a very subtle air of your letting the good lady win as that's the gentlemanly thing to do but you could crush her like a fly really. If you manage that lemme know how to do it, being trying to master it for ages when she hands my ass to me at High Velocity Bowling and Guitar Hero