INFO

There is a lot missing from the story. Mainly, was your mom a part of your half sisters lives growing up?

Pending information, with the scenario as written, this is an ESH.

Your mom is an adult. She can navigate the relationship with your half sisters and set boundaries without your intervention.

The relationship between your mother and half siblings is theirs. If it makes you uncomfortable that they see her as a motherly figure, that is YOUR problem, not theirs.

Your half sisters showing up and yelling at your mother is out of line. You yelling at them to get the hell out is out of line.

Your dad is a straight up asshole.