Not sure about putting nitrogen on as dog spot is basically already a case of fertilizer burn.
It's just the cost of female dog ownership. It's not anything in their urine, it's just the behavior of how female dogs pee, while males go around peeing on everything - a little here, a little there. I have (had) two large dogs in a small yard. Half the lawn turned yellow and died. Tore up that half and reseeded this past spring. Came in real nice but already showing a couple dog spots because the old girl is so lazy and uses the same spot and doesn't get around that good anymore. Never had any luck with watering in to reduce the concentration of the urine.