Is it permissible for me to secretly take my share of the profits without my partner's knowledge, after agreeing with him to split the profits equally, in order to avoid conflict and severing kinship ties?

This transaction falls under partnerships (sharikat) and profit-sharing agreements (mudharabat), and it is valid. If the capital is from both parties and the work is from one of them, then a higher percentage of the profit can be requested. Otherwise, what matters is what was mutually agreed upon. If the partner does not agree to that, then you are not permitted to secretly take anything from the company's funds, and he is not unjust as long as mutual agreement exists between you. Mutual agreement on equal division to preserve brotherhood and kinship is a commendable act, because strengthening the bonds of communication and love is the most noble thing to strive for. One must beware of cutting ties and turning away from each other.