Looks like you were off to have a fun day! For the occasional towing of that rig to the trail, I don't see any problems as long as the tongue weight is appropriate.
"Bad" tow vehicle isn't the rumor. "Sub-optimal" is more like it. I've towed loaded 3-horse trailers and can still do ~60-65 uphill on the freeway. But it's not comfortable, you're always watching the rpms and temp guage, thinking about the tranny, wondering if it's going to start pushing you around on the downhill s-curves, etc. It tows, and does a decent job at it when set up with brake controller and air bags (non-AHC). It's just that if towing is something you're gonna do every weekend, or every day, then there's better solutions out there that don't have the compromises. Oh yeah, 8-10 MPG doesn't help the rumor either.... Can it tow?, yes, of course, but that capability is not in the "strong" column. Short wheelbase and small V8 are the biggest downsides. The 5 speed is much better than the 4 speed when it comes to towing, too.
Now our horse towing is done by my daughter's 7.3L F350 4x4 Crew Cab long bed. It's a MUCH better routine tow vehicle, but a pig off-road. Every vehicle has compromises. I'm an infrequent tower, and I find that it's still stressful for me. I never hop out after towing anything in the Cruiser for several hours and think, "man, that was a enjoyable, relaxing drive." A sub-optimal vehicle just adds to that stress, not reduces it. Maybe that worry goes away if you tow every day? As I tell my horse-trailering, 20 year-old daughter, when things go wrong towing, the consequences are almost always brutal, severe, permanent, and frequently involve other people (or your animals), and a heavy trailer just exponentially amplifies the bad outcomes from things that normally happen. The checklist is ALWAYS to be followed, every time, no short cuts, never "just this once" or "it's only a few miles".