Is forgiveness of the offender appropriate even if it involves slandering one's mother, and is it permissible to retract such forgiveness, especially in matters of slander?

You may forgive the offense of cursing as it pertains to your own right. However, the slander against your mother is her own right, and she is the one who possesses the authority to forgive it. The punishment for slander is not dropped except by the forgiveness of the slandered person themselves. Your forgiveness of your own right does not require retraction, nor does it affect your mother's right.