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This letter sounds a little like the plot of the book Love Walked In -- absent/uncaring father, little girl abandoned by her crazy mom, young stepmom forced to step in.
Anyway, I think that both the LW and her boyfriend are horrible jerks. I said it. Horrible jerks. First off, what kind of parent barely sees his own kid? And second, what kind of person thinks that a neglectful, uncaring parent is a suitable mate? Why would you consider marrying a person who can't muster up the ability to parent his own child?
I feel really sorry for the little girl in question, and am glad that she has one person in her life who cares about her -- the nanny who was paid to do so.
The LW needs to leave her boyfriend, since she's not ready to be a parent. And the boyfriend needs to man up and do his job as a parent and take care of his daughter.