Good luck.

I went threw a very similar ordeal. I was charged with a DUI last June -
- its an instant 24hour probation
- 90 days licence suspension
- potential to face criminal charges, another year of licence suspension, and possibility of icbc installing a breathalyzer in your vehicle

I got my licence back after 3 months and ICBC took it away again even though I did not receive the notice, but that was due to a prior speeding ticket.

Highly suggest getting a lawyer, and what he will most likely due is offer a plea bargain with the court, which will turn your criminal charge into a motor vehicle charge (driving without due care) seems like my lawyer could have done more but he kept saying "at least you dont have a criminal record"
All in all, paid 5k for the lawyer and 1k for the ticket. Finally after one year I am going to be reunited with my licence in mid June. Shitty year without a licence for sure.

Hope everything works out!

if it truly was the police departments human error, sue in small claims for damages arising from having your vehicle towed (eg, opportunity cost, grief, etc)

another example:
it would be a huge cost if you were planning on selling your car, but since they had it towed, you could not sell it.