What is the ruling on the Dhuhr prayers performed by the questioner, given her doubt about the return of urinary incontinence, and does she have to repeat them?

If you are not certain that urine or other impurities were discharged after ablution, then your Dhuhr prayers on those days are valid. This is because your ablution is certain, while the impurity is doubtful, and the fundamental principle is that certainty is not removed by doubt.