Personally, I would keep looking. As stated above, it is in an average state of (dis)repair, given its age.
Look for one in an above average state, you will get to using it a lot faster. The list of what you will want to do to either of the trailers you have seen so far will be long.
A few thousand more spent now could get you a much better interior, and perhaps some already-replaced appliances. On the ones you have talked about, you will definitely have to replace the lot: furnace, water heater, stove-top cooker, voltage converter, AC unit, and the refrigerator (refer), or at the very least, the cooling unit of the old one.
Start looking for TTs in the $8k to $14k range. Oddly enough, your total investment of money should be far less that the ones you saw so far. Your additional cash investment will save you time lots of time, which will let you get out on the range and enjoy camping much
Your family will love it too!