So her problem is
not how they treat her but how they treat each other? lol
If they treat your GF just fine, she needs to accept that family dynamics are different across the board. If your mom's cool with the way your dad speaks to her, then that's none of her business. If your GF cares so much, maybe she should speak up and ask your mom about it - it'll probably be an eye-opener to learn that your mom and dad have more defined roles and act as such (oldschool) and it works just fine for them.
After that, tell her she
has to go and she needs to respect your authoritah.