Because spending out of community property income comes equally from both partners, neither provides more than half the support, so neither can claim the dependent.
You use IRS form 8863 (get the form and instructions here) to claim the American Opportunity Tax Credit, which is based on qualified college expenses that you pay for yourself, your spouse or a dependent for whom you claim an exemption on your tax return.
If you pay someone to watch your qualifying child or dependent (generally, a child under age 13) while you work or look for work, you can, in theory claim the Child and Dependent Care Credit.
Today's visit to the Clyde by Defence Secretary Philip Hammond included a claim of 1, 200 jobs currently dependent on the next generation of nuclear-armed submarines.