That will depend on what her death certificate says. If the death certificate says her residence was Florida, then only the Surrogate in Florida will probate the will. Likewise, if the death certificate says her residence was Philadelphia, then only the Philadelphia Register of Wills will probate the will. If your mother was only visiting Philadelphia when she died, then she was still a Florida resident. If she had moved up here and then died, then she is Philadelphia resident.
If the information was filled out incorrectly on the death certificate, and you did not catch the error until after the funeral director sent in the death certificate, it can be corrected by petition though the Department of Vital Records.
If you have any other questions about probate in Philadelphia or Florida, feel free to contact our office for a free consultation.