The ticket is legal, although it will be an interesting trial.  Hiring a lawyer might well make the difference between being found guilty or not on the DUI, and that is definitely worth the cost.

Based on what you've written, you're not guilty of DUI, only leaving the scene of the accident.  However, the problem is that your story is what lawyers call "self-serving," meaning it sounds like it's set up to protect you rather than being the truth, and you'll have to establish and defend your credibility to have this story believed.  That's where the lawyer will make the difference, if it goes to trial;  there's also a fair chance that with an attorney, the prosecutor will agree to accept a guilty plea on leaving the scene and dismiss the DUI.