How unfortunate that your mom got cut this way.
This article says that anti-inflammatory corticosteroids (like prednisone) can inhibit the proper healing of wounds. Perhaps being offs meds (or further reducing the prednisone, if possible) could help your mom regain some of her natural healing ability, but I'd be very surprised if that kind of change would happen instantly.
With only a rash, it seems that she hadn't had serious GVHD skin issues, but the biopsy may reveal more information about it.
You might ask the dermatologist or plastic surgeon if they think this type of result from a serious cut (a non-healing wound, dead skin, and the need for a skin graft) is common or uncommon given the type of cut. If they say it's common then your mom may simply be the victim of an accident that could have happened to anyone. But if they consider this unusual then it's definitely important to let the hematologist do a full study.
In either case, you should hear from all of these doctors before deciding whether a skin graft is the only (or best) choice.