Hopefully you and your wife purchased UM (uninsured / underinsured motorist coverage). You also want to obtain the police report and review it to an experienced personal injury lawyer. They may be able to see other responsible parties. There may be a road design or construction defect.
The answer is always "It depends." How much insurance does the driver have? The more in coverage, generally the longer it takes. You are not at "maximum medical improvement" so neither your lawyer nor the insurance company can clearly assess the value of your damages. The DUI element is a big issue in evaluating your damages but not the only one. Even a "quick" settlement can take 6 months to a year.
The likelihood of a recovery depends on a lot of information not contained in your post.
Such as the speed of the other car, the damage done to your car, the amount of medical care needed and the length of time your injuries affect you.
Sometimes minor injuries turn out to be more significant than first expected. However, insurance companies will argue that if you didn't go to the doctor or didn't follow up with another doctor than you must not of been in pain. Even a week or 10 day gap...
You have a police report. Take photographs showing the damage done to your car.
You'll need an experience trial lawyer to represent you if the insurance company is denying liability. You should ask lawyer about trial experience.
Evidence can disappear if you don't hire a good lawyer to preserve it.