Tricky situation...please advise

What is the name of your state (only U.S. law)? Massachusetts

I hired a plowing company to plow my driveway this winter. It also happens to be the same company that plows my neighbor's property (a retirement home...a very rich and powerful company in the community).

This retirement home threatened to terminate the plow company's employment with them if they continued to plow my driveway. The reasoning that was given is that the retirement home and my landlord are having a dispute over an incident that happened over a year ago.

My question is: What are my legal rights in this case? I hired the plow company and pay fee out of pocket...I am not reimbursed by the landlord in any way. My feeling is that the retirement home has no right to blackmail the plow company into denying me service based on the fact that I live in a building owned by someone they are having a dispute with. Isn't this a violation of my right as a paying customer?

No. If the plowing company wants to continue plowing your driveway, it may. If it decides to stop plowing your driveway for whatever reason (except those reasons prohibited by law - things like your race, your gender, or your religion, but not something like threats from a retirement home), this would be perfectly legal. Just because you're willing to pay them doesn't mean that they absolutely must work for you.

It's unlikely that your neighbor has an employment contract with the plow operator.

They can choose who they buy from, and who they don't buy from.

I choose not to buy from xyz store because they sell candy to children. If I tell them I don't like selling candy to children, and they stop, the children cannot sue me for blackmailing them.

It's really the same issue.

This is a consumer issue, not an employment law issue. And if the plow-er chooses to give up your business to keep a much bigger account, that's his choice.