How can a non married father who keeps his daughter 50% of the time file the child care credit on his tax return? He pays all day care expenses. 10,000$.

My son has a daughter (3). He and mother were unmarried when she was born. Mother claimed her first year, he claimed her 2nd. The mother stopped working this past year and my son has more income this year. He has her 50-51% of the time and pays probably 75% of her expenses including all her child care expenses which totaled $10,100 this year. How can he claim the child care if mother claims the child as the dependent this year. She has told him she will file early and is going to file her as a dependent regardless of reason.