In all likelihood, the latter (calling every hospital). If it were a VA or a KP, they may all be in one place, but that would assume all [old] records were put [scanned] online about 10 years ago, which is just newer than when both of those systems got their current online health records. Big assumption.

Your bigger hurdle is HIPAA. Unless the rolling stone filled out a release, they may be sealed for good unless Mama bear's doctor requires something specific from a specific place and even then I wouldn't hold my breath.
Sorry.