Not to be negative but there is no chance you will gain access to a nuke anytime soon. First and foremost you have a drug/alcohol related charge in the past 5 years (DUI). Second, you were in rehab but also just got discharged from the Navy, for being impaired, after that rehab took place. Last but not least, you were just denied access at a nuke which is kept in a database that all nukes use. Some nukes are more lenient than others but in your case I don't see you gaining access at any nuke.
My suggestion is get your life in order and give it all a little time to pass. In most cases any drug/alcohol charges in the past 5 years are always going to hurt your chances, especially when there are multiple charges.
You will have a chance to gain access again one day assuming that you keep out of trouble. It just won't be for a while.
Good luck to you