The main issue is probable cause. Why did the cops...
...knock on the door to begin with, let alone barge in when you opened the door? Even if the woman was the most famous hooker in Denver, that doesn't give the cops probable cause to think a crime was being committed. You could have been her husband or BF for all they knew.
You don't have the same expectation of privacy in a hotel room that you do in your own home. But even if hotel management recognized her, she was BCD with you and not creating a public nuisance. Unless you were swinging from the chandelier and making a lot of noise, there was no reason for the cops to knock on your door.
And where is the "solicitation?" The cops did not see the exchange of money for sex. She was not an undercover cop and I highly doubt that the room had a hidden camera.
You said "City D.A." Cities have City Attorneys, counties have District Attorneys. The distinction is important because a city attorney may be prosecuting you under a local city ordinance while the D.A. may prosecute you for solicitation of prosecution under 18-7-202 c.rs. This crime is listed in Article 7 of Title 18 with other offenses related to "morals." As qwerty said, it is a Class 3 misdemeanor which is a step above jaywalking but conviction under this code section could be problematic for your immigration status.
If this was a bigger crime, your attorney would have made a separate Motion to Dismiss based on lack of probable cause and there would have been a hearing on the motion before the trial date. But he'll probably make the same motion on the day of the trial before the trial begins.
City attorneys don't want to have jury trials on Class 3 misdemeanors. When push comes to shove, they'll offer a deal at trial.