you are in such good hands, my dear. your mother not only gave you life, it sounds like she continues to save it and nurture it. this is not something that mothers do automatically or without a price to pay. it is a choice they make and they do it at great personal cost. you will see this more clearly if and when you become a mother yourself.
the focus of your thoughts on your dad is understandable. i truly believe your dad loves you, but he is not capable of showing it in a safe and meaningful way.
the fact is your dad is sick. this is the kind of illness that spills over onto those around him and can do them great harm. this is what your mother is protecting you from. there is physical harm like from a drunken wreck. then there is the mental and emotional harm. that rollercoaster of love/hate being generated by his actions is not good for a developing child. like bending a young sapling, that bend will be in that oak tree a hundred years from now, forever a part of that tree.
i dont have enough information to know if your dad is a narcissist proper, but the tendencies are there. that is not important anyway. that is important is what you chose to do with what you know. your dad has sent mixed messages to you. well, every message must have a transmitter and a receiver. and like a radio, you can listen to some stations and never tune in to other ones. you know the goofy sixties station is there, but you pass right over it and dont spend your time listening to the archies sing Sugar sugar. you instead listen to the station that makes you feel good, the one that you identify with, the one you can talk to your friends about and read about in magazines.
this is the gift your mother has given you. instead of being forced to listen to the emotional rollercoaster station, you now have a choice. the station is still there, she cant change that. she cant stop you from thinking negative thoughts about her or your dad, but neither are you forced into it.
you also need to decide who your dad is. i never knew my biological dad and i tell you, i have the best dad in all the world, alive and well. i am lucky that he is all i have ever known. that other guy isnt a dad. in fact, i was in my forties when i was told(after my mom died). imagine that! i never knew anything and yet it still effected me, so i know how you are torn. you have to decide, "does this define me, or do i define it?"
you need a dad to show you how a man treats a woman. if you dont consider carefully, you could soon find yourself with a guy just like Frank and with a little girl just like you. its your choice.