Well, first I guess I should explain why we chose to spell it Madeleine ourselves. The answer is quite simple: that's how it's spelled. It's French in origin, and Madeleine is how the French spell it. They use it for small cakes, there's a river Madeleine, a village called La Madeleine, and a church, Église de la Madeleine, in Paris. Madeleine is the French form of Magdalene, which is Hebrew for "woman from Magdala". Magdala is actually Aramaic, though: it's a small town in Galilee from where Mary Magdalene is reckoned to have come; it means "tower".
So why Madeline?
Here's why:
Madeline is the heroine of a series of 6 children's books by Ludwig Bemelmans, an American author of Germanic origin. His first language was nevertheless French, so quite why he chose to spell the name the way he did I don't know for sure. I suspect, though, it was to get a rather weak rhyme: "In an old house in Paris, that was covered with vines, lived twelve little girls in two straight lines... The smallest one was Madeline.".
In the USA, where even back in 1919 children were named Madalyn, I don't suppose this was a great variation from tradition. However, it's caused the Madeline spelling (if not the pronunciation) to propagate such that people now believe it's the correct version. Some even think that Madeleine is from the name Madeline.
So it is that my daughter is doomed for the rest of her life to have to tell people they've spelled her name wrong.
It could be worse, though. She has a friend at school called Ceejay.