You are FLAT OUT LYING. Had you stated that you child could die if his food was prepared on the same stove as meat without it being thoroughly cleaned between, they would have politely informed you they are literally INCAPABLE of complying with your request.
Additionally, being vegan IS NOT a medical condition and 99.99% of vegans could eat a 1/2 lb steak with no adverse effect. Also note that outright food poisoning takes more than 2 to 4 minutes to have an effect.
IF your child began to feel ill in a few minutes, and didn't actually die in less than an hour, that is nearly conclusive proof the cause was something that happened before you stepped foot in the restaurant.
If he was anywhere near as allergic to meat as you claim, merely being in the restaurant would have made him ill, and that is YOUR fault, not the restaraunt's fault.
By the way, while it is possible to be allergic to specific meats, there are exactly ZERO know cases of being allergic to all meats,