You have to understand that they have to be thorough when it comes to vetting for a police officer, they can't afford to initiate the wrong person into the force as ultimately it is a position which requires upmost trust.
Initially on my phase 1 vetting I was declined on the basis that I was a witness to a crime when I was only 13 years old. I did later appeal and the decision was overturned after I provided a detailed account to the incident.
That example just goes to show exactly how meticulous they are when it comes to choosing the right person for the job. And let's be honest, most police forces aren't short of applicants so they can afford to be picky.
I understand how frustrating this must be for you, my advice would be to, if you can, appeal the vetting decision and write out an email explaining the situation exactly and what the circumstances were. Unfortunately though, urinating in public is a crime, so it won't help your case that you were caught doing it twice.
It's a real shame but there's no point lingering on something that you can't change now.
Hope this helps.