Is it permissible for a son who previously relinquished his right to the apartment to now take something from his mother out of fairness, or is his relinquishment irrevocable in Islamic law?

It is permissible for the son to accept his mother's gift, which she intends to use to achieve fairness among her children, and his previous waiver does not prevent him from doing so.

However, he must treat his mother well and not argue with her or raise his voice at her. Rather, he should explain the truth to her gently and kindly, as Allah commanded in His saying: "And your Lord has decreed that you shall not worship except Him, and to parents, good treatment. Whether one or both of them reach old age [while] with you, say not to them [uff] or repulse them but speak to them a noble word. And lower to them the wing of humility out of mercy and say, 'My Lord, have mercy upon them as they nurtured me when I was small.'"