Bill,
There are a few tests you should do before spending any money:
1. Check the ability of the Laptop to play a DVD film. If the laptop can play the DVD without any gaps or glitches - then that means it can process and display the video transport stream at a fast enough rate. Any playback glitches then forget it.
2. Now place the laptop in the caravan where you think it would be best - and play the DVD again. Move around the seating area and see if you can still see an acceptable picture on the screen.
Laptops and TVs have different screen technologies - generally laptops screens ensure that people can't sneak a peek over your shoulder, and TV screens so that everyone can see.
You'll just need to test your screen. Any colour loss or colour inversion - forget it.
3. If your laptop passes these two tests - then look for a review in Which or the Internet for a digital TV adapter. They are not all the same, and it's best to make a short list of the better ranked models.
Then remember that you'll probably have a few more wires, external speaks and bits floating around (and that may not be convenient), that you most probably won't have a remote to adjust the sound or (possibly) the channels, and finally that the quality of the PC tuners isn't the same as that found in a Sony or Panasonic TV - but is probably similar to a no-name TV
Robert