Obviously, you have at least towed once with it to mention that it is a bit sluggish..
First, it will feel sluggish when towing, even if you had a 400 HP engine.
Towing takes a lot more energy to get things rolling and that will zap your off the line "hole shots" you are used to when not towing.
While I sort of agree with the small motor assessment, that isn't really all of the issue. You have a vehicle with a curb (empty) weight of just under 5,000 lbs, it will be matched with a gear ratio less suited for towing.
To put this into perspective, I towed a 20ft travel trailer with a 97 F250 with 2valve 5.4 rated 235 HP with 3.73 axle ratio and curb weight of truck was 5,500 lbs.
Trailer empty weight was 3,600 lbs, loaded for camping was 5,000 lbs.. The truck did tow the trailer, was very slow getting rolling from dead stop and 7% grades were a challenge often downshifting to second gear and maxing out at 45 MPH up those grades.
The 97 did tow my trailer, but it was slow, used a lot of fuel and really made the truck work.
2003 changed trucks to a 2003 with same 5.4 equipped similar but for that yr the HP was upped to 265 HP, the 2003 performed better, pulled the hills better and was able to pull 7% grades around 55 MPH with the same trailer.
2006 bought a new truck equipped with 3 valve 300 HP 5.4 and what a difference, handled a newer heavier trailer evem better.
When towing you need to dial back your expectations on how quick it will be in getting started from stop to up to speed. You need to dial back your stopping expectations also, even with electric brakes on the trailer the extra weight will require more stopping distance so if you are used to tailgating folks, don't do it while towing..
You need to dial back your passing expectations, your not going to be able to shoot out into the passing lane and get up to passing speed as quick as you are used to when not towing.
You have now joined the slow turtles so sit back and relax.
With some practice and patience on your part, you will find a sweet spot in getting rolling that your motor and transmission will be happy with.
Don't get me wrong, more motor does make a difference, as it has been said, there is no replacement for displacement..