Again, horrible judement was used, but does this constitute dismissal? Since you were dismissed, yes.
Is there a first amendment right that covers me in a conversation with a coworker in this case? Freedom of speech means you can criticize the government. It doesn't mean you may use a racial slur when speaking of a student without any repercussions from your employer.
I just cant believe 20+ years of doing everything I can, and fairly treating every one of my students, 6+ years of schooling (masters +20 credits), and one word can take my career and hard work down? I'm afraid it can.
What recourse the school district takes is entirely up to them. No laws prevent them from terminating you over this lapse in judgement. If there is any appeal process with the school district, you may want to pursue that but nothing illegal occurred when they terminated your employment.
A person, who is nice to you, but rude to a waiter, is not a nice person. (This is very important. Pay attention. It never fails.)