Is it permissible for a sister to financially assist her brother in holding an engagement party in a wedding hall that includes singing and video recording, knowing that she fears falling into sin?

If the celebration includes unlawful singing or mixing, it is impermissible to hold it or assist in it; due to Allah's saying: "And do not cooperate in sin and aggression." One can refrain from providing assistance for this purpose, or stipulate that there should be no religiously forbidden elements. Pleasing Allah takes precedence over pleasing people.