Is it permissible to attend an engagement party where there is music and singing, while playing the Quran loudly through speakers to avoid hearing the music, in order to please one's mother and avoid her intense anger, knowing that attempts to advise them have failed?

It is not permissible to attend a wedding that includes forbidden singing, unless it is possible to sit in a place where this objectionable act cannot be heard, while also denouncing those who are present. One can go to offer congratulations from outside the venue of the celebration, or before it begins and then depart. The family will be convinced that you will not participate in disobedience to Allah.