I had to deal with a similar issue with one of my former employees. Here is the way that I understand this law.

You should not have been terminated for entering treatment rehab for alcoholism. You should have been offered your allotted ammount of time for FMLA (which is considered to be unpaid time off). While on FMLA, the employer cannot discriminate against you. Prior to entering rehab, your employer should have provided you with the necessary forms for FMLA. If he did not, your documentation from rehab, and the paystub you recieved on 3/14 should be sufficient in proving that your employer was aware that you were entering rehab, and that they were negligent in not offering FMLA.

Furthermore, my understanding is that alcoholism can be considered a mental disorder, which is protected under discrimination (I am not sure what part).

The employer was not required to pay you for any hours missed while on FMLA for entering alcohol rehab. Any payment that you recieved from your employer was a good faith gesture. However, your employer should have allowed you to use any unused vacation time (if any).