Have a look at Exchange Impersonation.
You can have a specific user account impersonate another user account and access their details without the need for their username and password. This should work on resource calendars as well.
string impName = @"impy";
string impPassword = @"password";
string impDomain = @"domain";
string impEmail = @"impy@domain.com";
ExchangeService service = new ExchangeService(ExchangeVersion.Exchange2010);
service.Credentials = new NetworkCredential(impName, impPassword, impDomain);
service.AutodiscoverUrl(impEmail);
// This will work as if you are that car.
service.ImpersonatedUserId = new ImpersonatedUserId(ConnectingIdType.SmtpAddress, @"CAR1@domain.com");
More references: http://msdn.microsoft.com/en-us/library/dd633680(v=exchg.80).aspx