I pulled my Roo 19 (~4000 lbs loaded) with my 2011 Chevy Traverse (5200 lb tow capacity) for one season. I was NOT a happy camper. Got a 2009 Silverado (7500 lb tow capacity and longer wheelbase). Much better.
Biggest issue with the Traverse was drag, not necessarily the weight. Also, you'll be going to a shorter wheelbase, meaning more bobbing up and down.
I would not pull it with a Santa Fe. Get a new truck.
1988 Coleman Sequoia - popup (1987-2007)
2012 Roo19 - hybid (2012-2015)
2016 Mini Lite 2503S - tt (2015 - ???)
2011 Traverse LT, 3.6L, FWD
2009 Silverado Ext Cab, 5.3L, 4x4, 3.73
2016 Silverado 2500HD Dbl Cab, 6.0L 4x4, 4.10