Retroactive child support is based is based on an order for your father to pay your mother while you were under the age of 18 and still in high school. If he failed to pay at that time and your mother had to foot the bill for all of your expenses while you were a minor, she earned a judgment for his failure to pay. Consider that money repayment for the money she paid raising you, you have no right to it as an adult.
I agree with the above answer, you have no legal right to that money. Perhaps you can ask your mom to loan you some of that money. However, if she says no, then you are not going to be able to take legal action against her in attempt to recover some of those funds.
This answer is intended for informational and educational purposes only and should not be considered legal advice nor constituting an attorney-client relationship. This attorney is licensed in Texas.
As that is between your mother and father, I would look to your situation instead.
Are you receiving child support from the father of your daughter every month and health care? If not, that would likely be a substantial help in paying for her day care expenses and other expenses as well. I know its easy to look to our parents, but the real responsibility is between your daughter's mother and father. How old is she? Has he ever paid? Is he behind? Does he work? I hope this helps.
This is just an opinion, and is no way to take the place of an attorney that knows all the facts of the case. Therefore, I would seek such advice as soon as possible.