She's pretty hell bent on having her own computer, lol
Girls like things that are "theirs". I bought the wife a Laptop and she's not allowed to touch my PC.
Anyhow. You can install Origin on any machine as well as BF3. However, you can only be logged into one machine at a time with your account. So if she is logged in with your account on her machine, you can't be logged in on yours. It makes your account portable, but the game license is still attached to you... or at least your account.