If you truely have joint custody in that the child is with each parent 50% of the time, and you share the childcare expenses 50/50, then most parent switch off years with claiming tax credit on child care AND as a dependent. I don’t know if you can split the childcare costs. That would be an accountant question.
Now…in my case. We have ‘joint custody’ but I am the custodial parent, meaning the kids stay with me 75% of the time. Ex has every other weekend, plus Wednesdays, 2 weeks in the summer and shared holidays. In THIS case, I am assumed to be the one to claim the kids as dependents and have claimed child care expenses in the past. You can do whatever you want in sharing that tax advantage, but legally, if you are the CUSTODIAL parent, you have right to the dependent claim.