Our trip to Tenerife was exactly like this. Our driver was wonderful and with us being the last pick up one of us had to sit in the front so I did this. Our driver was from England, in fact we were pretty sure he was Michael Barrymore, and whilst everyone else looked out of the window and seemed to be completely shy I spoke to him about the fig trees, the landscape and so on.
Our only concern about a 4x4 trip in Cyprus was the boys. We didn't know if we had made a mistake booking a trip where we would be in a confined space with other people all day. However! Imagine our delight when the driver, Akis, turned up and referred to us as the VIPs. We thought he was just having a joke with the boys but we really did feel like VIPs as we had the Land Rover all to ourselves!
Our driver was amazing, he told us a lot about Island life and I think one of the best things was how personal it was, specifically because he was telling us about the knock on effects of the banking crisis and how the currency changing to the Euro affected the island.
Akis really looked after us, made sure we were ok, answered our questions, we talked about the differences between school life in Cyprus and in England (he has 3 children all in education there). We felt really lucky to be able to have him to ourselves really as I can't imagine the experience would have been AS amazing if we were part of a big group all squashed together.
At one point the driver called to me and said "Hey, Are you enjoying your massage in the back there Mama?". Sitting in the middle seemed to be the bumpiest and the rough mountain terrain did mean we were constantly getting thrown around the back of the car so I'm glad I didn't have to have that personal interaction with complete strangers.
Our driver also helped us to stop at a pharmacy to get Charles some cough syrup. It was him doing things like this that really gave the trip that personal touch. He went into the pharmacy with my husband to make sure we got the right stuff, and then encouraged Charles to drink it despite it being disgusting!
He was amazing with Harry too, and I needn't have worried about taking the boys on such a trip. Harry held his hand as we visited The Baths of Aphrodite and Lara Bay. He helped Harry put his coat on a few times and Harry took a real shine to him and they were like best friends, which pretty much meant I was able to go off and take photos as I wasn't needed!
We booked our trip through our Thomson rep, although after searching Google I think these can also be booked independently. However, because we booked through Thomson this meant we had lunch included and this isn't something that is usually part of the deal.
I think this day trip is one we will never forget.