Some women love being SAHM. Some need to have their careers. A friend of mine worked 2 days a week. She said it made her a better mother to work part time but she didn't want to work full time.
The flip side of the male/female dichotomy - women CAN stop working or work part time whereas in our society men generally can't.
Every woman is different. So is every couple. There is no "right" answer. Ultimately, if you are not sane, your daughter will not have the mother she deserves. You gotta take care of yourself first in order to be the best mother for your child. If that means you go back to work full time - then do it.
Thankfully you have a good partner. It's hard that your daughter seems to love him more, but she needs you more. It's an important distinction. But fostering her strong connection with her father is good for both of you. And taking time away from her is not neglect when she is with a father who adores her.
I was Daddy's girl, but I still needed and loved my mother. Nowadays she is one of my best friends. Don't compare your daughter's relationship with Dad with her relationship with you. I know, easier said than done... but it's the way to sanity.