Q. Can I enter education/misc expenses for my child but still let my spouse claim the child deductions?
A. No. All tax benefits go to the parent claiming the child as a dependent.
That's not technically correct, but for your purposes that's the bottom line.
For tax purposes, there is no such thing as joint (50%) custody, regardless of what your legal agreement says. The requirement, to be custodial parent, is that the child live with you MORE than 50% of the time. One of you has to be the custodial parent and the other the non-custodial parent.
It is allowed for you to arrange the child's schedule so that the child spends more than half the year with the father one year and more than half with the mother the next year so that you are each the custodial parent (and Head of Household) in the year you claim the child, so that you can claim full benefits.
Of course, you can get away with calling yourself custodial parent / Head of household, if you both agree to do it that way.
It's not clear what deductions you were trying to claim. The most common one that would cause conflict is the dependent care credit. And yes, that can only be claimed by the custodial parent (under your arrangement, the one claiming the dependent for that year).
