Is it permissible to partner with a brother who works in selling alcohol in America to build a house for the family, knowing that the cost of construction will be equally divided between them, and neither of them can complete the project alone?

Your brother's work in selling alcohol is forbidden, according to the hadith: "Allâh has cursed Khamr [wine/alcohol]..." His salary is ill-gotten wealth. He must repent, quit his job, and dispose of this money by giving it to charitable causes. It is not permissible to partner with your brother in building a house with his ill-gotten wealth.