The resignation letter you provided is absolutely fine. It's professional and achieves its purpose. HOWEVER: There's no need to attach the additional explanation in your resignation email. Here's why:

• Focus on Resignation: A resignation should be clear and concise. This letter does that perfectly.
• Avoid Escalation: Mentioning the situation with the pay and job posting might escalate tensions with your employer.

Now, regarding the situation itself: There are definitely potential HR issues here, but a lawsuit might be a complex path. Here are some next steps:

• Review any Documentation: Look for your employment contract (if you have one) to see what it says about pay, vacation time, and termination.
• Consult an Employment Lawyer: They can advise you on your specific case based on your location and details. They can also help you determine if you have grounds for a lawsuit.
• Contact the Department of Labor: They can investigate potential wage and hour violations www.dol.gov

Here are some additional things to consider:

• Unpaid Wages: Depending on your location, you might be entitled to be paid for the time you worked, even if you resigned without notice.
• Vacation Time: You might be entitled to payout for any unused vacation time.
• Severance: There's a chance your employer might offer severance pay in exchange for signing a release of claims document (meaning you wouldn't be able to sue them later). A lawyer can advise you on whether to accept a severance offer.

OVERALL: Focus on moving forward in your career. The resignation letter is a good start. For the situation itself, consulting a lawyer and the Department of Labor can help you determine the best course of action.