Is it permissible to spend a sum designated for God from business profits to marry off needy relatives, and is it necessary to inform them that it is charity, and should a needy relative who is extravagant in his marriage be given?

You must fulfill the promise to donate the specified amount for the sake of Allah. If you intended a specific beneficiary, then it is obligatory to give it to them; otherwise, you have the option to spend it on charitable causes.

Giving to needy relatives is better, as charity to them is both a Sadaqa (charity) and a Silah (maintaining kinship ties). It is not necessary to inform them that it is charity or a vowed donation.

Money should not be given to someone who will use it to disobey Allah or to someone known for extravagance and wastefulness. Instead of giving them cash, you can provide them with what they need to ensure the charity is used appropriately.