It depends what you mean by a reasonable amount of space, and lots of miles.
It's just I do wonder if potentially, neither car would be quite big enough for a family.
The T-Cross is a small car; it's basically a Polo on stilts.
The Q2 is a little larger, but not much -- it's best to think of it as an A3 hatchback with a little extra cladding.
If your DCs are little under 7 or 8, say the Q2 is the better shout of the two you mention. Its Volkswagen equivalent would be the T-Roc.
You could also look at the Volvo XC40. Or I can highly recommend the Mazda CX-30, which is a similar size. (Personally, my general preference is Japanese makes over European ones, mainly for reliability reasons. That said, Volvo does well in the reliability stakes.)
If DC are a bit older, I might be inclined to look at a slightly larger car so you've got more space for them and their stuff as they grow; Subaru Forester, Honda CRV, Mazda CX-5, Volvo XC60, Skoda Kodiaq maybe.