Is it permissible for me to consider the zakat on my financial assets as zakat due to me, because others have refused to give me zakat, and therefore I do not pay it out, considering it instead as compensation for the zakat due to me from my brothers?

It is not permissible to give Zakat to children or parents, because it brings benefit back to the payer, as if he paid it to himself. As for your statement: "I took the furniture by law," if you are the one who took it, then present the matter to the people of knowledge to clarify its legal ruling.