My mother home schools my daughter, by the way, and she lives with my mom and dad. I almost live with them, as I am over there every day and tuck my daughter in bed every night, and have her for the weekends, but we found that it is more "peaceful" if I can have a place to go (I have a little apartment about 5 minutes away from my parents' house) if we hotly disagree about something (occuring less and less frequently).
I hope my daughter turns out as lovely and respectful of his mother and grandparents as you are!
My mom lived with my grandparents for the first year of my life and they completely supported her. Obviously, you have a similar situation.
I would love to share all the sacrifices my mother made, but it would take too much space! Suffice it to say, I know now that my mother DID make great sacrifices for me.
Growing up, I just knew my father wasn't a part of my life, that he didn't want to be a part of our lives. It wasn't anything I dwelled on. My mother always put it as us, together, so I didn't feel like it was just me he didn't want. I knew that my mother didn't know where he was and couldn't reach him if she wanted to. Maybe it was because I grew up in the 70s, or maybe I was just naive, but I never thought about where babies came from, or that my mother wasn't married, or about sex. My mother said the hardest part for me was father-daughter events at school. About five years after my grandfather died, my grandma remarried and my new wonderful grandpa took me to father-daughter dinners and dances. I will always remember those times.
Anyway. I started questioning more as a teen-ager, and started blaming my mother for my dad not being around. She didn't give me a straight answer for a long time, and I resented her for it. I didn't think that it hurt her, or that maybe I was too obnoxious, or that I was being a rebellious brat, or was using the issue to be a martyr. Finally, after I tormented my mother for two years and turned her gray, I asked my grandmother. I was 17. She told me the truth. My father had been separated from his first wife when he and my mother met each other. They dated, and in fact double-dated with two people who I knew -- one was my Godmother. I found out her husband was my father's best friend. None of this I knew, yet I saw them several times a year growing up.
I found out my father had another daughter -- I had a half sister who was four years older than me. I had more information than I ever had before. My grandma also told me that my grandfather, my real one who died when I was 2, tried to find him, but he had left the country to avoid paying ailmony and child support to his first wife.
I called my Godmother's husband, without telling my mom, and he filled in some more details. When I turned 18, I started looking for my father. I actually found my half-sister first. Then, I met my father for the first time when I was 18-1/2.
We are as different as night and day. I am a conservative Catholic hardcore Republican; he is a communist. I don't use that term lightly. But at least I know where I get my political activism! My mother is completely apolitical.
After I met him, I told me mother everything. I know it hurt her, but I wanted to know everything, the truth. She told me he wanted her to have an abortion, and she wouldn't. She said he left the country and her father had hired a private investigator to track him down, but couldn't find him. He was suspected of being a drug runner, smuggling marijuana from Mexico to the U.S. My Godmother's husband told me he had come back to the country, but didn't know where he lived. I told my mom I would meet him again, but I didn't know where it would go from there.
After three or four meetings, I knew that I could never have a relationship with the man who fathered me. The clincher was that he lied to me. He told me flat out that he didn't know I existed. My mom told me he did, and I believe her. My godmother's husband told me my father had actually asked about my mom and me after I was born. So he definitely knew. If he couldn't admit that to me, I couldn't have a relationship with him.
As to your daughter, she probably knows a lot more than I did. Never lie to her, but give her age-appropriate information. I can't say I wouldn't have been a brat as a teen-ager if my mother had answered my questions when I first started asking, but I wouldn't have had that as an excuse for my bad behavior.
Know that whatever you do, you have God's help. Don't do it alone. You have your parents -- they love you, and your daughter. I would, personally, move in with them and deal with the family squabbles. You need to be there for your daughter when she has nightmares, when she is sick, when she just wakes up and wants to talk about something. I know it's hard -- my grandmother had a mind of her own! -- but the times I lived with my grandma and mother were the best in my childhood. You might want to consider a family therapist -- a Christian therapist -- to help with the rough spots.
Good luck, and God bless. He is watching over you and your daughter and loves you both, and is proud of you.