Give yourself time. Don't overthink any of this. That is how the WT dudes came up with their stupid ideas.
Your little girl is singing about loving Jesus. . I think it is less scary to focus on loving "baby" jesus when one is a little child. Or less creepy. Kids are kids and love everything. They are happy and joyful. Our JW parents were thunderclouds over that holiday and tried to ruin it for us forever, but the basics of Christmas for believers is sweet and about faith, not stuff. Your daughter can get a taste of that sweetness. Whether it sticks or not, she is going to have sweet memories rather than bitter ones at the holidays. You may never be able to change your gut entirely, you have been programmed. But you can insure that she never has the uglies associated with a holiday that should be positive, even for irreligious folks.
I gave my mom a cranberry bliss bar yesterday and feared she would refuse it because it was a seasonal item for christmas (She didn't!-but seriously, who could refuse one of those?) Your daughter is not going to have to worry about wearing too much red in December, or putting lights up at her house or being caught in the christmas paper aisle at walmart by an elder. She will eat christmas cookies with no guilt unless she is dieting (another thing I'd steer her away from, weight obsession). Let her have that. You can give her that gift, if nothing else.
It took me about 15 years before I stopped thinking about it all the time at holidays. As above, I still get twinges, but not gut wrenching ones. You have a good future.