Mustard gas from peeing in bleach....
The answer is "no." Mustard gas will not be produced. Mustard gas is ClH2C-CH2-S-CH2-CH2Cl.
Some people warn against combining ammonia based cleaning agents and chlorine bleach. They are concerned that toxic chlorine gas will be produced. They are misinformed. Ammonia is NH3 and bleach is a solution of NaOCl. Together they produce a gaseous (but water soluble) compound called chloramine, NH2Cl. Chloramine smells somewhat like chlorine, and is the odor you detect often in indoor swimming pools.
Urine is primarily urea, CO(NH2)2, with very little ammonia. (If your pee contains a lot of ammonia, then you are one sick puppy.) But, pee that's been around awhile will increase in ammonia because it is a waste product of the action of bacteria on urea. The pee in the pool causes the production of ammonia, which combines with the NaOCl used to disinfect the pool and chloramine is produced. It also means that the pool is "sick" and needs some serious attention.
The bottom line is that urea, a compound with nitrogen, cannot be turned into mustard gas which is a compound containing sulfur and chlorine.