pumabob, have a look at the General Conditions on the Grimaldi website, although the section under "ACCOMPANIED VEHICLE" isn't 100% clear, but they do mention appendix and tow-hook though. I'm not sure for definite, but I think that I saw a car with a small trailer on the way down to Malta from Rome.
If you only have personal belongings in the car / trailer, you won't be classed as commercial, how you could prove that is another matter, but that will be no problem. And you'll have no worries regarding size restrictions, 90% of the vehicles are huge lorries and you'll be up parked on the open deck. There was even an Irish guy transporting pigs when I went back to Rome and he had a twin-lorry, i.e a normal lorry with a second container connected as a trailer, and even he managed to get parked, albeit with some difficulty.
I would check with Grimaldi via phone or email that taking a trailer is OK, but it should be alright. When booking an oversize vehicle, you just have to insert the total length (car + trailer) in the "VEHICLE EXCEEDING ON OF l. 6m, h. 2,10m, w. 2m. " field. It's 30 euros per metre per journey. That bit confused me a little, I couldn't understand if I was to put in the overall dimensions, the number of metres over the maximum, but for oversize they are only interested in the length.