From a "What's actually installed" standpoint, it's said there is no difference between what is installed with an upgrade disk and what's installed with a "full" disk.
The difference lies in how each are used - one (your's) is valid only to upgrade a current Windows install. Your sister's is valid for any install (one at a time of course).
Can you, physically, install from her disk and use your product key - probably. It might take a call to MSFT to activate but it can probably be done.
Should you (is it legal)? Unless you are updating a Win7 install, it's probably not legal. And, if you are doing an upgrade, skip the hassle - just use your disk.
Using the routine outlined in a previous post, you will get the results of a "clean install". And, no, if done right you will not have any Vista residue.