If you want to tow 2000#, I can't think of anything better than a Subaru. Either a Forrester or an Outback. You might have to allocate a little bit more money though...
Another vehicle that will tow it is the Chevy Equinox, but it bigger, hence the fuel economy is not as good.
If $4K is the max, you might look for an older Quattro.
Clearly your constraints are a challenge. You'll have to spend a lot of time on the various websites, to find what you want.
Mike...
P.S. You don't say where you live, but there are some options here:
http://www.voaautosales.com/inventory.php
The quality is remembered long after the price is forgotten, so build your teardrop with the best materials...