I was a cop for 24 years. I cannot imagine what was going through this guy's mind when he thought this was a good idea.
On duty, in his patrol car engaged in "activity" with a transvestite prostitute. Mind boggling doesn't quite do it justice. Complete douche bag comes to mind. As does criminal.
Be who you are. Be what you are. Just keep it legal and keep it the hell away from the job knucklehead.
Fire this puke. Fire him now and then prosecute his sorry butt for solicitation. Dude, you really piss me off.