Is it permissible to count the amount paid to resolve a dispute between a cousin and her brother as part of the annual Zakat, considering that the cousin is among the poor and needy, and that she will not receive her full right from her brother until after some time?

The intention for zakat is a prerequisite when it is disbursed. Therefore, if one gives money with an intention other than zakat, and then later wishes to count it as such, it is not valid. If you did not intend it as zakat at the time of giving, then it is not sufficient. However, if you did intend it as zakat, then the situation of the beneficiary is to be considered: if your cousin is provided for by her husband's maintenance, she is not eligible for zakat. But if she is in debt, it is permissible to give her zakat as a debtor (gharimah), provided that the debt is paid off. The disputed amount between her and her brother is not considered a debt owed by her, and it is not permissible to give her zakat on account of it.