Can I sue If I was served a real burger after requesting a veggie
I agree that this inquiry significantly overlaps with the post of which this one is marked by NuclearWang as possible duplicate. Thus, the answers (such as why breach of contract is inapplicable) and comments provided there largely apply here. I will only address the slight differences.
I walked up to the cashier and asked was this a veggie burger? He said
no. I stated that it was I ordered. He said he would make a new
A claim of fraud would fail in court because you will be unable to prove that the restaurant knowingly misrepresented to you (that is, despite knowing it to be false) that it was serving you a veggie burger with the intention that you would rely on that representation. Two hints indicate that the restaurant didn't act with that fraudulent intention:
(1) When asked, the cashier told you that yours was not a veggie burger; and
(2) he promptly indicated his intention to mend their mistake by telling you that he would make a new burger.
A claim of Intentional Infliction of Emotional Distress (IIED) would also fail. You wrote:
After we left, my daughter who was still in the restaurant stated that
they started laughing at my husband and I.
The fact that the employees waited till you and your husband left reflects that they refrained from intentionally inflicting any emotional distress. A significant factor that will favor them is the fact that they stopped laughing once your daughter asked them why they were laughing:
My daughter asked why were they laughing, when her parents were in the
car sick from eating meat. They stopped laughing.
Even if you genuinely feel disrespected by their subsequent laughter, there are no legal remedies because their laughter insofar an expression was neither obscene nor disparaging nor threatening/harassing. Laughter can be an understandable way, and possibly a psychological need, to relieve the stress from a situation like this in a context of hours of hard work in exchange for low wages with which to pay their bills.
Moreover, the same fact [that they waited till you and your husband left] contradicts the allegation that they laughed "at" you. Strictly speaking, the restaurant could viably sue your daughter for defamation if the restaurant incurs any losses (including court-ordered sanctions against the restaurant) as a result of falsely attributing to it the hostile or belittling behavior implied by the particle at. By this I intend to illustrate how certain actions under pretext of extreme "sensitivity" can backfire.
People elsewhere are victims of much worse misconduct or offenses that have detrimental effects and long-lasting ramifications. The court system is --if only in theory-- intended to redress wrongs which are more serious than a mistaken order at a burger restaurant.