you absolutely can step back from your parents at this time. it sounds like what you shared with your mom (in private) really struck a nerve with him and he is lashing out. your mom did not maintain your confidence but stuck a stick in the wasps nest and now wants you to LIE about it.
toxic. unhealthy. and not good at all for your peace of mind and sobriety. i suggest you seek other sources of support and give the folks a wide berth.