I am considering buying Minecraft Pocket Edition for my two kids. They share an iPad. Does MPE have a way to log in so they can each play separately on the same device?
No. MCPE has only one account, you can have multiple worlds on it though.
If they share the same iPad, the worlds will be place together but you can have many different worlds with different names so your children can play on their own world. Consider buying another device if you want them the play with each other.