can 2 separate xbox live accounts play via one xbox360 device?

REWRITTEN (why is there no edit option)

Hello, my brother and I play offline with one xbox360 console and 2 remotes in same game with 2-player mode. Our dad purchased one xbox 360 gold live account which we play by taking turns. Our dad wants to know if  by buying a second xbox360 gold live account we can both play at the same time using the same xbox360 console on two seperate xbox gold live accounts on two remotes in same game. Can someone please confirm if this is possible or do we have to buy a second xbox 360 console?

If you want to play online multiplayer you would need to have two consoles.

Yes you can be signed into 2 profiles at the same time. Each profile will be signed into it's own controller.

Some games allow you to play online multiplayer via split screen.

It depends on the game that you want to play. Some games have multiplayer split screen where you can play on the same console but "most" games don't. It would be easier to just buy two separate consoles, but two Xbox Live Gold Profiles can be signed in at the same time on a single console.