If YOU feel comfortable, by all means go on the trip, I think there are alot of people who would not feel comfortable and even with cheap tickets/ accomodations would not fully enjoy themselves (your sister and mother among them)and therefore it may be better to re-schedule at a time the trip can be fully enjoyed.

At present, If I were traveling abroad I would also avoid any overtly American/British institutions and businesses that may be symbolic targets to the extremist terrorists.