Hi,
I do UCW and it's a really popular and brilliant treatment. But I have premises. Quite honestly I don't know how you'd do it mobile (but then I'm so disorganised I'm in awe of you who do anything mobile....)
The tank is extremely heavy - it has water underneath so you'd have to fill that at your destination but then it really needs to be on for a good hour to heat the clay solution through. You could probably use hot water in the bottom and hot water to mix up your clay to save time. Also, there's always a couple of inches of clay solution left so you'd have to throw this out each time so it wouldn't spill all over your car, which would be such a waste.
You'd need a couple of large crates for the dirty bandages (again very heavy once wet) and the suit and everything. It's a fair bit of washing to contemplate just doing it here and I'd hate the idea of having to get all that in the car and home to wash.
The ladies at Totally UK though are lovely and very knowledgeable - it might be worth giving them a call and asking if they have anyone doing it mobile you could talk to and/or any tips.........