Guessing a city ticket and not a criminal arrest, right?
http://library.municode.com/index.aspx?clientId=10649
versus
http://www.legislature.mi.gov/%28S%2...931-XLVIII.pdf
You're being pretty tight-lipped about exactly what you are charged with, and I don't know if you got caught red handed (insert any other appropriate anatomical part) in POV flagrante delicto, or whether you were just standing there taking pictures of her alone involved in nudity or sexual conduct, but it sounds like you got a ticket under 38-9-4 or 38-9-5 and both of them implicate prostitution - either a solicitation in a public place (did you negotiate the deal in a public place?) - or just engaging her for prostitution.
It sounds like the charge is under that city ordinance. You've got a chance to establish that filming adult content in Michigan is not prostitution and all you're risking to establish that is a ticket? That you plan to pay anyway? If Hal Freeman, facing a felony, had made a similar decision, the right to create sexually explicit content in California never would have been established. Shame on you.
The definition of "public place" under the ordinance seems to hinge on the probability that the public would see this, _not the police_. How likely was it that the public would see it? Isn't it true that the whole reason you picked this place was because of its seclusion? These kinds of statutes are designed to protect the public from seeing disturbing things like the court said in my state in People v. Haven. That's a second way of getting your property back.
Are you basically risking next to nothing by fighting it? Are there some odds that the prosecutor will back off once he sees that if you win, the "Open for Porn Business" sign will go up on I-94 to welcome the whole midwest to set up studios?
Look, I don't know all the facts, and I haven't even seen the ticket, but it all looks pretty chickenshit for you to plead out - on the basis of what you've posted.