So long as you follow federal laws pertaining to household employees, and any other state and local laws, rules and ordinances if any, that may apply, then no problem. Just remember that regardless of who you pay for childcare, money used from the DCS account just flat out does not count for the childcare credit. Only money that you have paid out of pocket and already paid taxes on count for that.
To bad G-Ma didn't come before July 1st with plans to stay with you through at least new years. If she did that then she would meet the requirements for you to claim her as a dependent provided her earned income (does not include social security) for the year was less than $4,100. If anything, that would get you up to a $500 credit and would have had the potential to increase your EIC if you qualify for that.
Personally, I'd pay G-ma as a household employee out of my pocket and save the DCS money for the daycare after G-ma leaves. With the cost of daycare now-a-days and depending on the account balance, it may not be enough to cover everything resulting in additional out-of-pocket daycare expenses.