Trusting a friend or the facts : (?

My friend whom I have know for five years now came to visit my family for a week. She stay in the house with us the whole time. We had 3000 dollars put up in the safe which is a combination lock but, we always leave it on the last number so we can quickly open it to get in it, so it is never really locked completely I guess you could say. Anyway long story short, the money mysteriously vanished when my friend went back home. The day after she left my mom went to get some money out the safe and it was gone along with some old coins which were also worth money. The money just didn't disappear so I confronted my friend about it and she pleaded with me that she love me and my mother very dearly and she could never steal from us because we are like family. I want to believe my friend but, my mother says she knows that my friend took the money. Now my mom has always had what you could cal a sixth sense because when I was a kid anytime she had a bad feeling about something in her gut she was right. Sometimes she would dream something and it would come true I mean crazy things like Sylvia Brown almost. Now I love my friend and desperately want to believe her but, all the facts point to her because I didn't steal from my mom and she didn't steal from herself so it had to be my friend. I'm scared that if I believe my friend my relationship with my mom will be strained and I know if I side with my mom I will lose a good friend. I really need honest and real answers because I'm lost at what to do. should I break all ties with my friend or what??