Just have to comment that if your DH is ruling anywhere out he is not quite the skier he would like to think he is - a very good skier will find excellent fun to be had in most places! (I've had fantastic trips to places with only limited skiing because we've found fun stuff to do - one time when the winter Olympics was on my brother and I spent a whole afternoon on one run trying to improve our carving technique using the 'sitting on a little stool' movements that Ted Ligarty does! Was fab, especially fuelled by cheap vodka. There were only 3 runs in the resort so we made the most of what was there.) That said, he IS being a ski snob if he thinks Andorra is rubbish. As people above have said, Soldeu has over 210km of piste, some reasonable off-piste if you know where to look, a couple of very good snow parks, an igloo hotel, and is hosting the World Cup there this year. The ski school regularly wins awards for being one of the best in Europe, and if you look up hotels like the Sport Hermitage you'll see there are several swanky spa hotels there these days.
That said, you can get a budget holiday many places if you plan far enough out. You will need lift passes, ski school for your kids, and equipment hire. These are guaranteed costs and will not vary much. After that you need to work out how to get there. Undoubtedly the cheapest way at half term is to drive (you can use Tesco Clubcard vouchers to triple up points and get your Eurotunnel crossing) but you can book to any of the airports reasonably cheaply if you book far enough out - keep your eyes and ears open for when the airlines release their tickets. If you pick a resort that is served by a less 'ski-y' airport (eg Barcelona for Andorra,) or has a lot of low cost carriers flying in and out you will have a better chance of finding a deal. My sister got all of her family to Ostersund in Sweden over New Year for only £90 per person.
Accommodation is usually my last consideration. I didn't book ours until a few weeks ago and I managed to get a reasonable deal in an Austrian hotel. However, the earlier you book the more choice there will be. If you are on a budget, I'd go self catering. Your kids are big enough to go out to restaurants if you can't face cooking. We got an apartment which slept 2 families in Konigsleiten last year over half term (which coincided with a big Austrian holiday weekend) for just over £3000. Our drive down and tunnel ticket came in at about £700 (huge 4x4, we had 7 of us in it with all our gear on the roof,) private ski instructor was £200 our child, lift passes were about £250 per adult and £150 per child, and only DS needed kit. So for our family about £3000 before food. We also had a long week in Sweden, again sharing self catering accommodation with another family, for about £2000, and that included car hire and was over Christmas.
Loads of ways to do it, but tell your DH to be prepared to go where you book with an open mind!