If you can't manage a signature on a form at the Old Pediatrician, the New Pediatrician should have a transfer of records form to sign. I would make use of the New Pediatrician's form if I just had no desire to deal with the old office at all whatsoever. If they require your husband's signature, so be it. Pick up the paperwork, have him sign, drop it off at your earliest convenience.
All of this should be able to be managed with your new doctor's office with their form. You really shouldn't need to pursue further communication with the old one directly.