Not only will it get worse before it gets better, but after it gets better, the same bad behavior will come back now and again, as she goes through developmental changes.
Fear not! Yes, you can recover your child from spoiling. I'm succeeding oh so slowly with my own 8 y.o. daughter. I had all kinds of emotional issues about motherhood when she was born (wasn't ready to be a mom) and when I finally got to be a full time mom, she was 3 y.o. I tried to make up for lost time by letting her do whatever she wanted. And if I refused her requests, she'd go straight to crying. Well, sometimes that broke my heart, but most of the time I'd give in just to get her to stop, because I hated the sound of it.
I took a class last summer based on a book about the whole authoritarian vs permisive parenting issue, "Positive Discipline", by Jane Nelsen. She shows how an authoritarian would react to a situation, how a permissive parent would react, and then she shows a better way.
Barbara Colorosso's "Kids Are Worth It" is very similar (and inspiring!) but less practical. She also describes the whole authoritarian vs permissive parents issue. She calls them "Brick Wall Parents" (your childhood home, Pamamidwife) and Jellyfish Parents.
You're doing the right things. Be insistant that she treat you with respect. Try to figure out why she chooses to hit and spit particularly. And don't forget the unconditional love!