Is it permissible for one to travel with his mother and sisters as their mahram, while knowing that the trip will involve impermissible things such as going to cinemas and mixed-gender restaurants, and that he might miss performing congregational prayers in the mosque?

The mother is the most deserving of good companionship, and showing dutifulness to her is more emphasized than any other act of piety. Obedience to her is obligatory unless she commands a sin; for there is no obedience to a creature in disobedience to the Creator. If the journey requested by your mother and sisters is permissible or religiously commendable, then accompany them and prevent them from committing forbidden acts. However, if you know they are traveling to commit forbidden acts, and you are unable to prevent them, then do not go with them.