Woody has a dynel sheath, dry rot has been repaired by current owner. She needs sanding , fairing and repaint on hull. I have verygood woodworking skills and done a bit of fibreglassing etc. So shouldn't be a huge problem , a little concerned about cost/time though. I have also seen a 16' which has just been completly redone same price range.
If the rot has been repaired then, yes, fairing, sanding and a repaint is quite literally all that's required. Compared to a similar task on a boat-in-the-water, a piece of cake. Also unlike a bigger boat, you can repaint the hull of a TS18 in a couple of hours and working on it at home (carport/garage) makes it a couple of weekend's work - and even un-faired and un-painted you could still sail it if you wanted to. Funnily enough, one of the original ideas behind the Hartley TS was that "father and son" could build one together in their back yard!
A TS16 is strictly a 2-person boat - sleeping in the cockpit under the stars. For the size of your family and what you are wanting to do, I wouldn't recommend it.
Having said that, the TS18 will be "cozy".. but the wife and I spent a week on ours one Christmas on the Gippsland Lakes without too much difficulty (*). One of the advantages of a bigger boat is more room, but the big disadvantages are (a) the storage of it and (b) that maintenance cannot be done at home. This can become a BIG downer if, for some reason, the family don't like sailing and the boat then drags you away from them in endless maintenance.
If you think of "Woody" as a short-term family-sail-training craft, you'll be fine. Also, because it is a "known boat" in the Hartley YC, when the time comes you should have no trouble selling it in future. If you and the family like her, make an offer and see what happens.
* = We were enjoying it so much we stayed out too long - until the food ran out and the Porta-Potti overflowed. Not fun!