No you cannot get a new passport without a your mothers signature. You could get a fake passport if you wish but they are expensive and hard to come by. If you get caught with one the penatly is 110000$ and 10 years in jail.

Plus as a minor when they do find you, since a missing child is a federal case which gives them access to everything including this very hardrive you are a minor and they will bring you home.

for the posters asking what you know about Islam, I somewhat agree. Despite Sharia's claims about equality of the sexes in a court of law a woman is considered half of a man. Husbands have the right to beat their wives. Women are constantly considered in need of protection from their husbands. They cannot choose their own husband, to travel freely or to choose their own clothes. Sharia and Western laws are combined in Egypt. I'm not saying you don't know this just that you can't say he will not be a controling, traditional husband without knowing him.