You raise an interesting question. Firstly the two is entirely civil in nature and your window for even bringing a cause of action is very limited. It may be even less than ten (10) days. Reference your paperwork to make sure still have time to file.
I have done a couple of these hearings for clients. First, its an administrative hearing and the burden of proof is much less. The officer just needs to be able to reasonably state they felt that they had enough evidence to detain you on suspicion of DUI.
There is much more to your story than you have told, but field sobriety tests are universally suspect - here you have an armed police officer in total command asking you to perform tasks you may not normally do under calm circumstances.
The biggest factor in your favor based solely on what you stated is that your BAC is below .08 which means the state cannot establish you were operating a vehicle under the influence of above the legal amount of alcohol in your blood.
Speak to your attorney about this. Each little village acts differently and it may be worth pursuing if the window is still open. Also, I have seen officers fail to show for these hearings and nothing elates a client more than a dismissed case or a fat check coming to them from the village for a tow.
Good luck. I will offer you a free consultation, but it sounds like you already have a DUI attorney. Unless that attorney truly just does not want to come out to that village for a few hundred dollars more, I'd ask them about this impounded car and tow reimbursement hearing.
This answer is marginal legal advice and does not constitute an attorney-client relationship. Every client and case is unique. The best advice is to always consult with an attorney. Free legal resources at www.ZippToCourt.com