Middle name help!

Our baby girl due in November will have 2 middle names, one for each side of the family. My husband picked "Frances" after his grandma and I picked "Michelle" after my sister. Baby will have my husband's last name, so he's insisting that we do my "Michelle Frances (Last name)" because there already was a "Frances (Last name)", so it's more obviously in her memory. I see his point but I also think "Frances Michelle" flows way better! It's a pickle. Suggestions??