if u get a visa for SA u will be fine. in fact SA has low criminality rate because of the punishment you could face. u should be properly dressed when giong there. going in short trouser is not done. go in long trousers and thin sweater with long sleeves. the last thing you want is to offend certain conservative muslims. I don't know if a scarf is mandatory (i know in Iran it is). so find that out beforehand as well.
cheers and good luck!
mel - sadly it's not even that they are going with my aunt. they are going alone.
Personally, I think it is a good sign, that your aunt is not going. I thought it was one of those awful situations, where she is in love with a not very good guy, and cant see straight because of it. Maybe she really just does not know what the laws in Saudi are like and thinks u and your mother are exaggerating.
Try your best to persuade the girls not to go. If this does not work, at least ask your family, to email u, as soon as the girls get back to the US, so your mind can rest, for at least some of your time in Japan.