Most issues with the Auto Park seem that it won't release. You have a different problem.
It might depend on the year but I believe the auto park system is a mechanical drum brake over around the driveshaft that's release by hydraulic pressure. Sounds like you have a mechanical problem with yours (problem with the linkage, excessive wear on it the pads, etc).
IMHO, you really need to have it looked it before you leave on your trip as it is probably not safe - the transmission is not strong enough to hold the vehicle on an incline and you need the auto park brake to hold the vehicle, if it doesn't your vehicle can roll.