What is the ruling on a veiled woman dancing at a wedding, and what should she do to expiate her sin?

The matter is easy. You must repent to Allah Almighty by not attending weddings where there are musical instruments. If your repentance is sincere and fulfills its conditions, then Allah will forgive your sin, and your misdeed will be erased, as the Prophet, peace and blessings be upon him, said: "The one who repents from sin is like one who has no sin."