RE: Collections - look into PFD (Pay for Delete) in the stickies and the threads here among other topics. You can probably get the identity theft ones cleared up too, but I'll let someone with more experience answer that one (DV letters, etc ad naseum).
That said, you want to approach things from both directions at once: cleaning up the reports but also establishing new positive tradelines; 36 months is a long time, but start now. I would think that any co-signed credit card application would probably overlook the negatives on her report with yours, since you're both jointly responsible for the debt and the assumption is someone with your lofty scores is a sure bet. Worth a call to their CSR anyway.
Add her as an AU to an established card absolutely, it's probably clean in your case (but just make sure), with a low utilization reported each month, and that's been open for a while. It'll help in this instance.
Beyond the Discover More, get her one or probably two (slightly better than one we think) more random cards, secured, unsecured, doesn't matter, you're just trying to establish payment history and the AU doesn't fully count in all situations.
