Okay, so my brother plans on getting Skyrim and I do too, but my PC can only run it because of the minimum settings despite running Crysis beyond the recommended ones. He decided to get himself a PC that can run the game and all.

But here's the question: if my brother have just the original game while I do have it's expansions (Dawnguard among others), if I play it on a shared PC with my Steam account, will I be the only one to have access to the plug-in (assuming my brother have only the original game)?

The DLCs are tied to the Steam Account.

If your brother wants to play the DLCs, he needs to buy them.