I understand your frustrations with this, but you're between a rock and a hard place. I agree with your lawyer's assessment. Realistically speaking I don't see how you can beat both the hit and run and the DUI. You're going to be convicted of one. Here's why:
Let's assume you don't want to plead guilty to anything but want to fight the case. The prosecutor is going to go forward with the felony hit and run and the DUI. You don't have a defense that I can see to the hit and run. You have an excuse, which is not the same thing at all. It does not make out anything close to a necessity defense which could get you an acquittal on that charge.
If a jury finds that the above was what you actually did, you would be convicted of the hit and run but not the DUI, and, of course, the jury could convict you of both charges, because if I were the DA I would strongly suggest that your reason for leaving the scene is that you didn't want the police to know that you were drunk. The judge would charge the jury that flight is consciousness of guilt and that will hurt you on the DUI case.
You might be able to find a lawyer persuasive enough to get the felony reduced to a misdemeanor
, assuming injuries and property damage was minimal, and to let you plead to that and dismiss the DUI as covered by the plea. It will be a hard sell, but you will know fairly quickly if the DA really plans on indicting the case.