"Right to work" has no relevance (otherwise it would be "no right to work"), but you are correct in that the facts you told us do not lead to a claim against the employer. They have no general duty to investigate or to believe you. You may have a slander claim against the other employee, and obviously you have damages. However, a valid claim is only the first step. One, you have the burden of proving your case and it is your word against his. Two, what if you win? How is a judgment against the other person going to get your lifestyle back? Does he have bank accounts, assets, etc.? What is it worth to garnish wages? Third, assuming you are in the market for a new job, how does filing such a lawsuit affect that effort? Finally, what if you sue and a judge or jury believes him?
I agree with Attorney Riddle. You could spend thousands in attorney’s fees and potentially lose. What your subordinate did was wrong and there will be a time when they have to atone for this act, but it is probably best that you try and move on. To remove any doubt you should at least talk with a local employment lawyer and see what your legal options are. Most give free initial consultations.
DISCLAIMER: David J. McCormick is licensed to practice law in the State of Wisconsin and this answer is being provided for informational purposes only because the laws of your jurisdiction may differ. This answer based on general legal principles and is not intended for the purpose of providing specific legal advice or opinions. Under no circumstances does this answer constitute the establishment of an attorney-client relationship.
If your subordinate falsely accused you of planning to kill the owner and manager, and you can prove it, then you could have a viable claim for defamation. You should consult in person with a local attorney to get a careful evaluation. It is the "at-will doctrine" that applies here, not "right to work." Good luck.
My answers to questions posted on AVVO are intended to provide general information only, and are not intended to be legal advice. Employment law issues typically require a careful case-by-case analysis. Consequently, if you feel that you need legal advice, I would encourage you to consult in person with an employment attorney in your area.
Regarding a slander claim, the other employee would probably have a solid defense: the intra-corporate defense. This defense, in a nutshell, basically says that no defamation occurs when the speaker (here, the other employee) and the hearer (here, the individuals in corporate) are a part of the same corporation/business/organization. In other words, statements made within a corporation are typically protected. Of course, there are a few exceptions, but they are hard to prove and I'm not sure they would apply to the facts you have listed. If you are intent on filing a slander claim, you should consult with a defamation attorney who can help determine whether you can get around the intra-corporate defense.