Driving is definitely the way with a teeny one: flying is such a complete pita and you get thoroughly messed around by transfers. It’s easy to stop every couple of hours and do feeds and you’re not so limited in the a mount of junk you can haul along. The ferry from Newcastle is a great relaxing start to the journey too.
I’d look for any of the valley based resorts as they tend to be larger and have better off piste distractions, so: ellmau, soll, les gets /morzine, zell am see, st Anton, kitzbuhel, anywhere in the Zillertal except tux. Also look at the jungfraujoch region (grindlewald, wengen, not murren or lauterbrunnen), though the lift pass looked frighteningly steep last time I checked. Chamonix is worth a punt too, but again bonkers expensive.
We take two cars and babysitters grandparents as ours are too weenie for crèches. Sister and bro in law do shortened days sharing babysitting with the olduns. I suspect well do the same.