We call our Alexandra Allie. It is in culture to name the baby full name and then call short name which in my country is Sasha but that did not catch up with my English-speaking relatives. The reason being is for them to get options with they name. They are called nick names when children, it stays like that with friends, but as they grow they use their full name to add formality. When my daughter started to learn to write her name her teacher insisted to write Alexandra and not Allie, because it was more challenging. We thought it was a great idea and again gave her options. These are some ideas, may be call her alexandra and let your husband a nickname to call her everyday. Alexandra is a beautiful name.
Ooh Andie is lovely. My favourite is Allie. I love Alexandra but so worried about her being called Alex which I don't find very feminine. I did consider Alexia or Alexis to avoid her being called Alex.