You cannot view a LR4 catalog with an earlier version of LR. The catalog database structure is different. Even if LR2 could open it, the LR4 raw-engine is creating different adjustments than the LR2 raw-engine understands, so it wouldn’t work. The difference between one LR version and the next is exactly the database structure and the adjustments.
She might be able to import the photos into her LR2 database, but the XMP files won’t necessarily contain the adjustments that LR2 understands, so she’d be seeing the default rendering, not your adjustments.
I think you would be best to export jpegs of the files for your mom. As mentioned above catalogs are not backwards compatible.