Thanks to USMC and GeeEssFore for the info. I started looking around for more info on the TPMS problem that I had, and was still a little baffled. It's amazing how many solutions there are for one problem, and sometimes you have to experiment to get to the right one. Any who, I finally got the whole thing fixed for just $33
instead of the $230 that the dealer wanted to charge me. Here's a detailed explanation to what I did for those that might have this same issue.
First off, I haven't figured out how to put my car's info in my signature so, as an FYI, I have a 2008 Jeep Commander Sport, 3.6L V6, 4WD, with the stock rims (not aluminum--I think).
Here was the initial issue:
Tire stem (not the core, as originally thought)
After more extensive searching online, I deduced that the problem had to only be with the stem and not the sensor, as they are two separate parts. Searching on Amazon, I came up with the thought that Schrader's service packs must be what I need.
The Stem @ $4.17
Other Service Parts @ $4.05
Before I ordered the parts, I went to a local tire repair shop to ask them to take the tire off of the rim so that I could remove the sensor and double check the parts. This $5 solution showed me that the stem could be removed from the sensor and replaced.
(The picture below shows the stem (silver) attached to the sensor (grey), after being removed with the large nut and rubber washer on the left.
After that, I ordered the parts, which arrived 2 days later.
First, I installed the new core (comes in the service pack) into the new stem with a Tire Valve Stem Core Tool (this tool does not come with the parts, but you can get easily at any local auto parts store for around $6)
This core is only half-way in the stem… use the tool to screw it down into the stem.
Don't over tighten the core, as it will break VERY easily, and you probably will not be able to get it out.
Next, I took the stem and threaded it back through the sensor (it will only go in one way). Then, I attached the non-threaded nut over the top of the new stem, and turned it until the flat ends fit into top of the sensor snugly (there's a small arrow pointing DOWNWARDS that should line up with a small line on the sensor as shown below).
Next, place the rubber washer into the large attachment nut (both in the service kit), so that the smaller end of the rubber washer fits into the nut.
Thread the new stem, attached to the sensor through the hole in the tire rim, and then place the large nut over the stem with the rubber washer side downwards, and hand tighten it to begin attaching it to the threads on the stem.
This is the view from the top once you get it on there.
Using a socket wrench and a 12mm bit, carefully tighten the large nut.
I then took the tire and the rim back to my local shop, who charged me $20 to re-attach them, fill it, and put it back on my car.
From this point, since I was using the sensor that was already on my car, I didn't need to worry about re-programming it. I drove for less than a minute, and the low tire light went off.
My suggestion is that if you get an entirely new sensor for some odd reason--try the 15 minute driving test (drive the car over 25mph for 15 minutes) before someone tries to convince you that you need to re-program the things. I've seen many sensors say that they don't need to be re-programmed.
Total cost: $25 for labor, $8.22 for parts.