The manufacturer has tested everything and certified the vehicle for towing that weight, so theoretically it’s fine. But as a mechanic I wouldn’t routinely push a vehicle to its max, especially with the added challenge of big hills, but once in a while would be ok, just be sure to go steady.
The added weight of people, a full tank of fuel, tack etc would actually be a good thing, the concern with towing at max is that it’s difficult to stop and the trailer could push past the vehicle, extra weight in the vehicle helps minimise that risk, although it is extra strain on the engine.
I plan to buy a car with a 2.2t tow limit, similar in that the trailer is 1000kg, Niko will probably end up 530kg/Jess is 580kg, we live in a really flat area so I’d take both in an emergency or very locally, but I wouldn’t do long runs/motorways/hilly areas with both and routinely it would only be 1.