People think very weirdly about unions. If you strip away all the fluff, a union is ultimately a business that sells labor, typically with a setup where the buyer(s) of that labor pay the labor directly, and then the labor pays the supplier, rather than having the money flow through the supplier first. The direction of money flow is unusual, but makes no practical difference.
All you're describing is an exclusive arrangement between a supplier and a business that buys from them. If it was a contracting agency instead of a union, and your family member was told that the only way to work in the store was to go through the agency, you wouldn't bat an eye. But call it a "union" and suddenly "he got squeezed."