>Twilight: overworked, can't set aside enough time for baby care (A Flurry of Emotions)
>Pinkie: not serious enough, can't properly discipline (Baby Cakes)
>Applejack: helicopter parent (Somepony to Watch Over Me)
>Fluttershy: too passive, doesn't have a high enough energy level for managing kids (Stare Master)
>Rarity: doesn't even entertain the possibility of caring for foals at all (Baby Cakes)
As you can clearly see by simple process of elimination, Rainbow Dash would be the best mother of the Mane 6 due to being the only one not being shown as a total fuckup at it.