Hello Marc
Choosing a car is very much a personal choice, but when trying to match it to a car especially with such a large caravan, your choices will be more limited.
We have to start with the caravan, and the crucial factor here is the weight of the caravan, which according to the Swift Website is MIRO 1679kg and the MTPLM of 1900kg.
It is always a good idea to ensure the tow vehicle is heavier than the trailer, but you must never exceed any of the weight limits of vehicles involved. The UK caravan industry advise novice towers should aim for the MTPLM of the caravan should not exceed 85% of the towvehicles unladen weight, so based on that calculation, that would mean you are looking at a tow car of about 2235kg ULW. This is only guidance, and the industry recognise that more experienced towers might consider approaching a ratio of 100%. Regardless
Either way with such a heavy caravan I think you will have to look towards a tow car with a ULW of 2 tonnes or more. This puts you into the very large luxury cars or 4x4's.
Whilst I don't think it applies in your case, but it's worth pointing out for other readers that for such a large outfit you must have entitlement BE or B+E on your driving licence.
Accommodating your dogs, means you will almost certainly be looking at an estate type vehicle. But this also has a knock on effect that you have less space in the tow vehicle for any luggage or kit. I would often suggest a large mpv, which offers vast amounts of space and reasonable handling, and relatively good MPG, but they may not have the necessary unladen weight to match your caravan.
You will also need a reasonably powerful vehicle. Most caravanners would agree that diesel engines are great for towing, mainly because of the torque the vehicle produces at low engine revs, but with the size of vehicles you need to consider, larger petrol engines are likely to be more than adequate, especially if you consider an auto gearbox.
There will be many contributors here on the PCV with experience of the larger 4x4's such as Range Rovers, Discovery's, Toyota's, BMW's, Jeep's and Kia's etc. A relative of mine uses a Mercedes M class, which may not be the biggest vehicle, but he finds it very effective as a tow vehicle for a large caravan, and he often has to carry two labradors.
Just a general note. Please don't assume that a big 4x4 will always remain in control of a caravan, capable as they may be, their bulk also means they can be less stable when pushed hard or when towing a big caravan.
I hope this helps