This is not how remote play works, it simply allows you to control the PS3 from the Vita from any location you have internet access.
Basically it displays what would have been on the TV screen on the Vita Screen but not every game supports this feature. You can however switch the PS3 on from standby and access the XMB.
Two player is not possible via remote play unless it is online.
Now that the Vita has been updated to firmware version 2.0 there is an option called 'cross-controller' under the remote play button. Apparently you need to download software from a game that supports this feature in order for it to work. I would assume that future games plan to use this feature.
I can't find any more information at this point, I just stumbled across it after I updated.