Your requirements are pretty similar to ours, just with fewer miles and budget, more towbars and snow.
Essentially the way I have searched for a car small enough for my wife to be comfortable but big enough to lug 'kid stuff' around in is to look at the boot space to length equation, which compact estates tend to excel in. This lead me to 308SW, Octavia Estate, Civic Tourer, Leon ST which all have boots around the ~600L mark but top out at around ~4.7m in length. Obviously with your budget you may be looking at earlier Marks so not all suitable. And of course not all boots are as practical as their size might imply, you also have to look at rear legroom etc (one annoying thing in our current car is that as my son is growing, I've had to move the front passenger seat forward a bit).
Regarding the 4x4 aspect one thing to bear in mind is that some cars have reduced boot capacity to accommodate it, so keep an eye on that if you choose to go down that route.