Thank you for giving me the opportunity to assist you. I will give the best answer that I can with the information provided.
I presume that your divorce decree is silent on the matter of who claims the children.
If she claims the children as dependents, she gets the child tax credit.
Who gets the daycare credit depends on who is the custodial parent. I know you are saying 50/50 split, but the year has 365 days, one parent has to have them for a longer time than the other. That parent is the custodial parent (in the eyes of the IRS). In order for the non-custodial parent to claim the children as dependents the custodial parent must sign Form 8332 or similar statement, or the divorce decree must be singed by the custodial parent and have similar wording as the 8332 (as long as divorce was prior to 2009).
The non-custodial parent can never take the daycare credit.
For purpsoses of medical expense deductions, each parent can deduct the medical costs for the children that he or she paid, regardless of who claims them for that tax year.
I know this is confusing. Please let me know if you need more information.