Maggi - how long do you have? Serious question! To put it in a nutshell (though it is open to debate) religious, economic, social and political influences were just some of the reasons why some fashions developed the way they did. For example during the Regency/Empire style of dress may have come about because of the French Revolution when it became dangerous, if not downright silly, to dress in extravagant silks and jewels. It may also have come about because of a new interest in antiquity. There is, imo, no one single factor that influences dress and hair styles but a combination of events and people who become leaders of fashion. So you could have, in your alternate history a leader of fashion - for example, to name a very few, Beau Brummel, Mary Quant, Coco Chanel. Their inspiration and genius changed the way people dressed.
See if you can get hold of The Language of Clothes by Alison Lurie - ISBN 0 7475 0821 6
From the blurb on the back cover "'Like most spoken and written languages, the language of clothes is constantly changing. New ideas and phenomena demand not only new words but new styles. ...most social political and cultural trends have been mirrored not only in what we say, but what we wear, so that even if we never followed the news we could guess at what was happening around us.'