Erasing all data before selling....

If her macbook is the same model it should work but if its a newer model nope. you will need to go to apple and get reinstall disks or purchase a retail copy of SL

 

Just choosing the "Erase and Install" option when you install will do nothing to protect you from the new owner accessing your data. That simply formats the hard drive, but that does not remove the data from the drive, it simply removes the information used to access the data. It is trivial to recover data from a formatted hard drive.

What you need to do:
When booted from the installation disk, before you install (after you select your language), choose Disk Utility from the Utilities menu. Choose to erase the disk from there, but click the security options button and select the option to do at least a 7 pass erase. This will write a series of 0s and 1s over your data seven times, making it virtually impossible to recover. The single pass will likely be enough to stop the casual observer, but why not use the extra security. This process will likely take a few hours. Once it is done, do the install as normal.

EDIT: I realize this doesn't answer your question about using your wife's disk (which is already addressed above) but a snow leopard disk is only $29 and that is a small tax to keep your data safe (especially after oddly throwing away your system disks. didn't you think there might come a time when you wanted to reinstall the os? perhaps, like, when you were going to sell the computer?)

 

My favorite part. Why do people throw these out? Do they expect to never have a single problem that requires them?