If you pass urine or drops of urine, this does not mean that you have to do ghusl. What you have to do is to make wudu and wash only the parts of the body and clothing soiled by urine. If the occasional emission of a few drops of urine is beyond your control, then the rules of urinary incontinence apply.

Touching dogs or their saliva does not break wudu because nothing can nullify the state of taharah except things for which there is evidence in the Shari`ah.