Children hurt. Children will sacrifice themselves for what they perceive to be the greater good, taking on the responsibility, the blame without even knowing they're doing it.
Parents protect, nurture, love and teach their children. Perhaps she needs more time with you, the limited weekends might be too little for a girl who needs her father. After all, fathers teach their daughter how to love, what to expect in a man.. among many other things.
Perhaps your getting stuck in the sadness, the funk you've experienced might have the same origin. It's easier to blame the spouse and bemoan what life has throw at us. Read up about 'visitor dads'. I don't know your circumstances or even if it's possible for you to give her more of what she needs.
Manipulating.. what if she is doing it? It doesn't make it wrong, it expresses a need she has, to be reassured. To know she'll always be loved. Only recently have I gotten my head outta my ass over the continuing loss of my marriage. It's my children's welfare that matters most over what was supposed to be a lifetime vow.
Guess what.. children ARE the embodiment of unconditional love and commitment for the rest of your life. At each turn of this winding rocky road ask yourself.. What is in the best interest of my child?
