Her school is very accommodating. Some schools do not offer extensions or incompletes, even with documentation for the Office for Disabilities. (Speaking of which, is she registered now with that office? That brings legal rights.)
The catch up within two months is also alongside other work? Or is she taking next semester off? How long is Christmas break?
How many classes, how many projects, is it very rigorous, and does she have tutoring or other help or is she expected to teach herself?
There is a difference between extensions (extra time) and incompletes. Either one, however, affords the chance to finish classes outside of the usual time frame, and incompletes should not show up on the transcript if the work is finished. If the work is not finished, they tend to convert to F’s.
If her mental health challenges were serious enough to merit treatment in an inpatient facility, I would talk to her and then talk to the school about a medical leave which should wipe her grades clean. Yes this means no grades for all the work she has done so far, but it avoids the stress of making up work, which is so important right now, and avoids the transcript having lots of W’s or F’s.
Measures short of that might include withdrawing from a few or most of her classes and finishing one or two. Again, with documentation, the school should not put W’s on her transcript.
I don’t know if she is on meds or in therapy. Sometimes meds can cause a quick turnaround but more often it takes time. Only you and your daughter know what she is up to in terms of stress and work. An argument can be made that returning to normalcy can be part of healing, so it is really a question of timing. Some kids go right back to college after a hospitalization like that.
And sometimes schools require a medical leave with interviews for reentry.
Good luck!
ps do you have tuition refund insurance?