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It sounds to me like the position of management is just their opinion that they want union contractors only. If so, the directive is not legal. It sounds like it is worthwhile saving this account. You will have to hire a lawyer to bring an action for a permanent injunction against management preventing them from interfering with your business. AND for a temporary injunction asap while the case is pending forbidding them from interfering with your business NOW since without that order, you WILL SUFFER IRREPARABLE HARM.
If you give me your state and nearest large city, I will get you a link to a directory we lawyers use to find highly qualified legal specialists in various fields at locations world wide. These lawyers are in the directory because they were rated as qualified by other lawyers in their field of expertise and geographic area.
I gave you the LITIGATION firms....just the 2-9 person firms. There are still over 200.
Here is the Labor and employment list as well: