My daycare provider gave me a weekly break down of fees paid for my children, but not per child. Can I estimate the amount part dependent or does it need to be exact?

You do not need to break it down "per child". or "per month."  You enter the amount you paid in 2020 for the dependents who received childcare and the tax ID or Social Security number of the childcare provider.

The daycare provider gave me the total amount I paid for both children, but on TurboTax it is asking for an amount per child. If it doesn't require a specific amount calculated per the rate for each child, do I just split the total 50/50 per child?

We paid $10360 - can I just put $5180 per child, or do I need to calculate what of the total I paid for child A versus child B?

Break it down 50/50 if you want.   You cannot get more than $6000 of childcare credit  for the two kids no matter what.