I'm not going to church with my gf after her dad died
Why would you not be there for her?
I have other plans which I don't have time for it
It's rude and very hurtful to not be there for someone when they are hurting. Your girlfriend needs you and you should be there for her.
She doesn't care about her father, it won't make a big difference to her. She can deal with it.
She shouldn't have to deal with it alone. Being with someone means being there in the good times and the bad and for the important things.