Is it permissible to give zakat to a financially capable sister whose husband is also financially capable, but who has children from a previous marriage and is struggling with their expenses and installments, while there are those who are poorer than her?

Your sister is not eligible for Zakat (definition) if her need stems from her extravagance and profligacy, or if she is able to pay off her debts by economizing on expenses. Likewise, she is not eligible for Zakat if her spending on her children is not religiously obligatory for her, such as if they are adults capable of earning, or if their father is able to provide for them. Zakat is not to be given to someone whose eligibility as a recipient is doubtful.