@john74,
Hang in there John, you are doing what you can for you daughter... and that is great. Remember that this isn't your daughter's fault, these parenting arrangements are stressful for kids.
Also, remember that your relationship with your daughter is a long term relationship. You will always be her father and she will want this relationship. Be super patient, and be available to her now and she will appreciate it later. It sounds like you are doing this.
Things change over time, it is likely that you will have a much better relationship in a year or two.
One more thing... when I was going through the difficult part of my divorce, my daughter and I had a couple of things that we always did together (that she liked). The cute, fun little rituals are not only fun, the provide stability and give her something to look forward to.
When my daughter was three, she went through an octopus stage. She wanted to draw octopuses with me every time she saw me (I drew thousands of the critters). I varied it up, sometime using crayon.. then pen... then octopus stickers and scissors to cut up octopus shapes out of paper... but always octopuses. She always loved it, it was fun to do and it bonded our relationship through some difficult times.
You might be able to find something fun that your daughter likes that will be the same. Kids love ritual and they love to do the same thing over and over again. Find something that she likes that you can do ... and go with it. Make it your special daddy-daughter time.
It takes patience, but you can do this.