Things that may help you in your search.
Tow Vehicle:
1. A vehicle's max tow capacity is calculated, considering the vehicle is a basic madel, with no aftermarket accessories, no passengers, no cargo, and the driver only weighs 150 lbs. It does not consider towing something with the aerodynamics of a brick wall. Towing a boat, is not the same as towing a travel trailer.
2. As the dealer and end user add options and accessories, the max tow capacity is going down, pound for pound. Then the end user adds passengers and cargo, and tow capacity goes down even more.
3. Payload is the difference between the vehicle's GVWR (Gross vehicle weight rating) and what the vehicle actually weighs (curb weight). It is also your capacity to carry the combined weight of accessories, people, pets, cargo, and tongue weight.
4. GCVWR is your rating for max combined weight of tow vehicle and trailer(including everything and everybody in, or on the vehicles).
5. Each (front and rear) axle has it's own weight carrying rating.
6. The hitch receiver has one rating for carrying tongue weight without weight distribution, and one for carrying tongue weight with weight distribution. Some vehicles, due to their frame / body style, are not recommended for use with a weight distributing hitch.
7. Tow vehicles of various makes / models are not all created equal. IE: One F150, Tundra, Titan, 1500 series, etc, may not have the same capacities as an identical looking model sitting next to it. It's possible to find two F150's, sitting next to each other, one with 5000 lb tow capacity, and one with 11,000 lbs. There's a version of F150's with only 750 lbs of payload. There's also, one
that can carry over 3000 lbs.
Trailer:
1. Dry weights are from when the trailer left the factory. Some manufacturers include a weight estimate for propane and battery(s), some don't.
2. Some trailers have options installed by the dealer, those are not normally included in dry weights.
3. Average camping load (dishes, pots and pans, camping gear, BBQ, bedding, groceries, and water, etc) is about 800 lbs.
4. Average tongue weight is 12.5 percent of loaded trailer weight.
The sceanario with your trailer and the Escape could look like this:
1. Max tow capacity rated at 3500 lbs.
2. People and cargo weight of 500 lbs, reduces tow capacity to 3000 lbs, which is the advertised dry weight of the trailer. If the trailer has any propane, batteries, or dealer installed options, that were not included in dry weights, you're over weight, and you haven't loaded the trailer, yet.
3. As you've seen, that could be an unpleasant towing experience.
When you shop for the new tow vehicle, consider your pre-existing payload and towing requirements. Depending on the weight of stuff, you intend to carry on camping trips, 5000 lb tow capacity, may not be enough. Find one where, after you deduct your payload requirements, it still has plenty of capacity (payload and towing) to carry / tow the the trailer weights. You might even give yourself some room for the next (bigger) trailer.
There are a lot of SUV's and trucks out there, that can do a fine job with your trailer. You just need to remember the not all created equal thing, and check the capacities of each candidate.