Should the profit from an inherited restaurant be divided among the heirs, or is it an exclusive right of the brother who manages it? And is it permissible for the sister to exclude her brother from managing the restaurant if he refuses to distribute the profits among the heirs?

When the inheritor dies, their estate—including the restaurant—must be divided among the heirs. The restaurant can either be sold and its price distributed, or an agreement can be reached to keep it and distribute its revenues after deducting expenses.

Your brother is not permitted to allocate the restaurant's income to himself without the consent of the other heirs, because each of them has a right to its income. Doing so is an injustice to them, and it falls under the ruling that prohibits a bequest to an heir, due to the Prophet's (peace and blessings be upon him) saying: "Indeed, Allah has given every rightful person his due right, so there is no bequest for an heir."

The brother should receive a management fee commensurate with his administration of the restaurant, and then distribute the remaining profit among the heirs, each according to their share. If he refuses to give the rights, the heirs are permitted to remove him and entrust the restaurant's management to someone else. In that case, he would only receive his share of the inheritance.