The hand that signed the divorce papers, IMO, is the same as the forged LFBC. In fact I am almost sure that the divorce papers signature is the origin of the LFBC signature.
That makes sense. I would assume that it is likely that SAD signed the divorce papers herself, but of course was not around a few years ago to sign the spanking new birth certificate. But then why did the forger have to do her name in bits?