My 2005 Ford Territory keeps shutting down when driving

Relatively modern, computerised cars like the Territory absolutely loathe low battery voltage. Without enough electricity to power all the fuel-injection and electronic ignition systems (not to mention the electric fuel pump and the on-board computers) the car will never run properly and is a good bet to enter limp-home mode as you've described. Other symptoms include the dazzling array of warning lights on the dashboard as the various on-board computer systems are left high and dry by a lack of voltage.

You're possibly on the right track with a replacement alternator as the 12.6 volts it's outputting is nowhere near enough to power the Territory successfully. Closer to 14 volts (at least about 13.7) checked at the battery terminal with the engine running and all lights and accessories switched off is where you should be.

Unfortunately, you've already replaced a whole bunch of parts that were probably okay. This approach of random replacement can ultimately cost you a lot of money you didn't need to spend, and a much better way is to have the car scanned to see if there's any electronic fault codes to give you a clue on what's wrong. But even if the alternator is not the sole cause of your problems, at 12.6 volts it is, indeed, worn out and should be replaced or reconditioned.