Rear latch, won't automatically open

SOURCE: Automatic door locks will not work.

you need to take it to the dealer and have them check the bcm for codes.... also have them check to be sure you have the latest software in the bcm.. its possible that you just need a software update... there are several TSB's covering the concern you have..... it can be a very simple fix with software or even a stuck lock switch may need to be replaced... without the proper diagnostic codes being read from the bcm all that can be done is guessing..and that can be expensive...

SOURCE: Crazy Electrical Problem in 2005 PT Cruiser

Either wire harness problems or you got a so called lemon
One of the first books of Ralph Nader about auto industry.

Had a Hyundai like that 27 years ago. Until I took it totally apart and re-assembled it myself. 2 years ago bought a Piaggio 45 cc motorbike, same story. Took that apart one night and put it together as should be.

SOURCE: the automatic rear hatch on my minivan will not

Take the inner door apart, and take out the lock mechanism. Chances are it is rusty. Clean it up, make sure all moving parts move, and oil it well. Put it back together and it should work.

SOURCE: Automatic locks do not work on doors but works on hatch.

This is a common concern that is only on the 2005 models. The problem is software related. The repair is to reprogram the body control module with a newer version that corrects this issue. Dodge had issued a service bulletin for this concern then can be performed free of charge if it is still under the factory warranty, if not then you will be charged for the repair which will be whatever the hourly rate is. The repair will only take one hour and does not require any parts. So they will only charge you for the one hour labour for them to have the vehicle. I'm not sure if your car is still under warranty or not. But it's also a rip off for them to charge you for an hour when they just hook it to a computer to reprogram it and then leave your car alone until it's done

SOURCE: 01 chrysler town and country fuse box diagram

that year was i think very close to the first year of all of the automated door openers and so on. when they first came out we had all kinds of problems with them. so its not a reach to assume you will have problems with the systems 10 years later [car sold in 2000] as for being related to your vibration problem i dought it. i would suggest cleaning or having throttle body cleaned if problem is at idle. clean it anyway it will give you problems later anyway. if engine vibrates at all or certain rpms then you will have to look at engine mounts or vibration dampner. as for the seat one of the tracks is missaligned with the other one. you have to remove seat and align tracks then reinstall.