I am always suspicious of men who try to undermine and put a stop to their wives'/girlfriends' ambitions. Usually they are inadequates who can't stand the idea of THEIR woman outshining them and not knowing her place. I wonder if this is what is going on with you.
I agree with PP: dump the partner, you can always get another one. And she is almost certainly transphobic, and that's what the hints about her kid are in aid of - bigots ALWAYS claim that people who are not like them are inherently dangerous to children.
NTJ and nor is your mum but you ARE a jerk if you don't tell your partner to go stick his head up a dead bear's backside and never contact you again. You do not need this man. Remembr, d*ck is abundant and of low value - you can always find a better partner so get rid of this one.