Here are some basic principles.
The FSA saves more money than the child and dependent care credit for a single person whose income is more than about $25,000. This is because the credit gets smaller as your income gets larger, but the tax savings for an FSA get larger as your income gets larger.
Head of household status is an additional tax saving but you must pay more than half the household expenses (rent, utilities, etc.) and claim at least one qualifying dependent.
An FSA can be used for put o $5000 of expenses no matter how many children you have. The dependent care credit covers $3000 of expenses for one child or $6000 of expenses for 2 children.
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For 2018 tax planning, there are too many moving elements to give a guaranteed answer, but this is my best guess.
Your partner should plan on claiming one child as a dependent, filing head of household, and using an FSA amount equal to the care expense for that child only (let's say $4000 each child). You plan on claiming the other child as a dependent and using the child and dependent care credit. This will cover a total of $7000 of your care expenses ($4000 FSA plus $3000 dependent care credit amount for one child). This will also make your partner eligible for head of household status and will make you eligible for earned income credit. The amount of extra EIC you would get for claiming both children will be less than his tax savings for filing as head of household.
For your care provider, you will need to get separate receipts for each child so he can get the right FSA reimbursement from his employer and you can each prove your care expenses if you are audited.
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For 2017 tax planning, you should test different situations, but my guess is you will do better if you each claim one child dependent. He can claim head of household filing status and the dependent care credit for one child, you claim single and the dependent care credit for the other child, plus you are probably eligible for EIC. The alternative situation (he files single with zero dependent and you file with 2 dependents) will give you a larger dependent care credit and maybe more EIC but he will lose a dependent care credit and head of household status.
Like I said, test it both ways.
