Would wearing headphones suffice to block out the music?

It is not permissible for you to attend such gatherings even though you will be wearing headphones, as you will be still be in a place where vice and evil is taking place.

Furthermore, by not attending such a function, this will not be tantamount to severing family ties. You may advise your mother in a polite way that attending such gatherings is against the dictates of our Deen.

Also, consider the following Ahadith:

“There is no obedience to the creation in disobedience to the Creator.”

“Whoever increases the number of a gathering, is part of them and whoever is pleased with/approves an action will be a partner of those carrying out the deed.”