any "two computer households" here?

Well, I've nearly gone and done it. Am trying to get a puter together for DW. Almost there!
I was wondering about the following:
We have two separate phone lines. I was gonna hook her system up to the line I don't use for business (the house line). That way she could get on the Net, have her own email etc.
I was wondering if I can just load the software my ISP sent me into her new system and let it roll! If I do, what happens if we both get online at the same time? (Her on one line, me on the other.) Will one of us not be able to connect, because the ISP sees I am already connected? Will I have to pay for a separate connection for her?

I know there is some type of computer sharing that people do when there are two computers on the same line, but what about two computers in the same house that are on separate lines?

Any ideas concerning the best (and cheapest) way to handle this?
Thanky folks!
Yours truly, sincerely, and (somewhat) dopey... ô¿ô