How can one tell a sibling that they will not attend their wedding? There will be music in that function, it will be a mixed gathering and I don’t think hijab will be observed as they are not religious. I will not feel comfortable. It will probably cost a lot of money to attend. I have nothing against the sibling, but I feel that I will be emotionally blackmailed to attend the wedding by the parent. How can one overcome this?

It can be done with respect and relying on Allah (swt). It will be difficult but if you place Him first He will look after you and reward you. Try to explain it politely and later visit them to congratulate the couple at home.