Interestingly (or not) the 2.2 in the 4007 is closely related to that in the TD4 Freelander 2, which leads me to suggest looking at one of those perhaps?
The S models don't come with terrain response, but all the others do, and there seem like plenty of 07/08 GS specs around at your budget from Land Rover dealers. Its no BMW inside, but everything has a nice chunky, solid, feel it to, and nothing has fallen off in the 6 months we've had it either! Averaged ~40MPG over 6months.
However are you sure any of these cars are right for you? We went to visit some family friends with young-ish kids (6 and 8) and yes they wanted to travel in the big Land Rover, and had great fun while they were in it, but watching them trying to climb in, while amusing once, would probably start to grate after about a week
Before we had the F2 we had a previous gen V70 T5, and that was far more child friendly IMO

A quick look on pistonheads says you might get a
current gen model just about in budget, or you can go for a late, mint previous gen with all the toys. They do have the turning circle of a small warship, but are much more fun to drive (relatively) than the F2 if only because they have a lower centre of mass.