Unfortunately, you can't. There is no splitting of benefits for a child. Whoever claims her as a dependent gets every benefit. Since he did not pay the expense, he is not entitled to the credit either.
You may be able to claim the child and dependent care credit if you paid expenses for the care of a qualifying individual to enable you (and your spouse, if filing a joint return) to work or actively look for work.
See this link for more information. Child Care
