First the word "Abusive" raises my hackles. Second, sounds to me he has made a threat by saying if you keep making payments "nothing bad will happen" not toward you but toward the child or mother or both. Gather your ammo and fight. As for not causing any drama for the mother........sweetie think of the child, how much drama will affect her, how much being in a family circle that possibly be abusive for her. Think if you don't do something how her life may be affected and not in a positive way either. Jesus I hate when I can't get my point across in simple words.
You need to get in touch with someone who knows how to go about things you can do for the better interest of the child. Wish I could be of more help.
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"Look into the mirror of your soul
Love and hate are one in all
Sacrifice turns to revenge and believe me
You'll see the face who'll say:
I love you... I'll kill you...
But I'll love you forever"
ENIGMA