Is taking out a percentage of the money from alcohol considered purification of it, and thus would it become permissible for us to eat and drink from the food and drink of one who does so, or does it remain part of unpurified money?

Selling alcohol is forbidden, even if there is no material gain, because it is an evil that must be destroyed. Selling it is a form of assistance in sin, and the Prophet, peace and blessings be upon him, cursed alcohol, its drinker, and its seller. The money earned from selling alcohol is unlawful and must be disposed of for the benefit of Muslims. There is no harm in maintaining ties with your relatives who sell it, nor in eating their food if they have disposed of the unlawful money. They should be advised to stop selling alcohol.