I don't want to meet my dad's new girlfriend
Why don't you want to meet his new girlfriend?
I want to know what her family thinks about me first
I understand your apprehension to meet you dad's new girlfriend, but it is rude to avoid meeting with a family member. You should give her a chance and figure out where you stand and if you like each other. If you cut her out, your relationship with your dad might suffer.
I guess you are right.
I am glad that you're willing to give his new girlfriend a chance, and I think you'll both hit it off!