What is the ruling of Islamic law regarding a young man reclaiming his right from his father who divided his home and source of livelihood between him and his brothers without his knowledge or consent, and should he waive his right to avoid his parents' anger?

Leaving your possessions as a trust with your father does not remove them from your ownership. As long as you did not intend to transfer ownership to him, they remain your property. Your reclaiming of your money is not an act of disobedience (ʿuqūq), because a father is entitled to nothing from his son's wealth beyond what he needs, and he is not permitted to take from it to give to other children. However, if you wish to uphold what your father did, out of devotion to him and charity towards your siblings, that would be a good deed.