There are many things wrong with turkey, but you can not longer blame it for making you sleepy on Thanksgiving. Yes, yes, you learned in science class that turkey contains the amino acid L-Tryptophan which is involved in the production of the hormone melatonin which controls sleeping patterns, which is why you need to take a nap on Thanksgiving afternoon.
But as Mental Floss points out, plenty of other foods contain comparable amounts of tryptophan, notably meat, cheese, yogurt, fish, poultry, and eggs. What’s really making you tired is your body making the extra effort to digest a really big, carb-loaded meal: “Overeating (especially of foods high in fat) means your body has to work extra hard to digest everything. To get the job done, it redirects blood to the digestive system, leaving little energy for anything else.” Alcohol helps, too.
So sorry, you’ll have to figure out another way to avoid your family. May I suggest washing dishes? You’ll have plenty of time alone in the kitchen and all that warm, soapy water is actually kind of therapeutic.