Islam has greatly emphasized on the rights of parents especially the rights and a mother, whether she be a Muslim or non Muslim.
It is only at the expence of disobedience towards Allah's commandments that a child is allowed to disobey his or her parents and that too should be done with utmost politeness.
One should always keep their moral behaviour and show warmth and kindness towards them even if they're harsh. Such a policy can change the outlook of a parent about their child even if they seem to disregard each others views generally speaking.
You are definitely facing a predicament on how to spend your time with two people who dont share the same faith like you.
If accompanying both of these people will lead to sin and you can stop that by excusing yourself politely, then it is incumbent that you do so.
If however your mother will take it to heart and feel much remorse, then you can explain her first about why you don't want to go, and if it were not for the music and other forbidden sins, then you would certainly accompany her in the trip.
If she still feels very bad about this that you feel it will completely spoil your relationship in the long run, then go along with her but at the same time try all you can do avoid sinning. You can do zikr and isteghfar ie remember Allah and ask for forgiveness when the music is heard, and lower your gaze when you see any one who is ill dressed and not Mahram ie lawful for you.
As for your friends, you can simply excuse yourself if you have to take your mother, and if not, you will still have to think of.anything but to let go off the probable awaited sin of falling into lust.

Remember they don't have any right as such over you and all the more so since they are non Muslims.
For humanity sake, you can still show your good behaviour and keep your relations with them but never at the expence of your faith.

Remember, the Almighty Lord is always besides you when you do the right thing.