I towed for 140,000 miles with a very similar-size and similar-power vehicle, a 2008 Toyota Highlander V6 with factory tow package. I had a KZ Escape E14RB, a 2700 lb (loaded) trailer, 16' long overall, 7' wide and 99" high. This size seemed like a good match for the HL and it only had a little trouble in the Rocky Mountains (long climbs at high elevation). Keeping the wind resistance as low as possible, by having a low, narrow profile trailer, will be a key factor in how these V6 SUVs perform on the highway.
Another key factor is hitch weight. My little TT had a hitch weight of about 350 lbs, but with a full fresh water tank it came close to 400 lbs. My HL's limits were 5000 lb towing with 500 on the hitch. I doubt I could have towed a 4000 lb (or more) TT because they tend to be well in excess of the 500 lb hitch weight limit of the HL (and a Traverse). One doesn't want to have a hitch receiver tear off at highway speed, sending the trailer careening across oncoming traffic (worst case scenario).
I grew up in MI so I know what it's like. My recommendations:
Get a TT with dry weight under 3500 lbs, preferably under 3000 lbs.
Get a TT that's no more than 7.5' wide, and maybe under 105" high (not counting A/C)
Trailer should be no more than 21' long, due to Traverse's short wheelbase
Make sure dry hitch weight is under 400 lbs, so when you add LP, battery, etc it will be under 500.
Keep highway speed around 55-60 mph.
You might take a look at a molded fiberglass TT like Scamp or Casita. They are rounded (egg shape) and move through the air much more easily than a conventional TT, they will yield better gas mileage (14-15 vs 10-11), and you might find them cute. A 13' or 16' model could be ideal for a single mom and child. I have found that small, lightweight trailers are more pleasant to tow and to maneuver than larger trailers.
For a TT longer than 17', you should get at least a sway bar, but better yet a weight distribution hitch with built-in sway control (Andersen makes the lightest, cleanest model IMO).