Dubai is SPENDY. I lived there and it is so expensive for everything except petrol, taxis and maids! February is a great time to go though as the weather is perfect then. In the summer it is hideously hot and you don't really go out.
If you like an alcoholic drink it will be even more costly. A couple of beers by the pool can set you back anything from £10 to £15 depending on the hotel. The cheap hotels are not really ones you want to stay in for a family holiday as they are usually in the older, busier parts like Deira and bur dubai. They will be old and a bit knackered too. I cringe now at what I used to think was cheap - you lose all sense of reality.
If you really want to go there on a budget I'd look into renting an apartment in a building with a good pool complex and in new Dubai (marina/JBR/palm), Jumeirah or the old town area (not old at all but a fake old looking part near the burj Khalifa)
Dubai has miles of lovely beaches which are free and you can find quiet areas, especially during the week so a beachside hotel isn't really a necessity. Plus taxis are plentiful - except on a Thursday or Friday night. There's a perfect cove near the Jumeirah yacht club where you could sit in total peace on weekdays. You can't access the beaches on the palm unless you are living or staying in hotels there.
Everyone raves about the shopping but as it's all mall based and expensive I couldn't be bothered really. Lots of british shops where the clothes are priced waaaaay more than here! Having said that Karama (an old area) is a fun place to grab a "genuine fake" handbag and practice some haggling skills. The malls are something though... Really damn impressive. There's not much of the exotic left although the museum is good.
Eating out can be wonderful - best food I've ever eaten in some of the places and the settings are stunning as most hotels are very grand. The madinat is especially lovely to eat out or have a drink in one of the bars that line the canals. You can get trips out into the desert where you dune bash, sand surf and watch belly dancing etc - actually great fun. But the best is a trip up to Musandam in Oman for a day out on a boat - you see dolphins and get to snorkel with the most incredible fish. The water is like aquamarine glass... So beautiful there.
For kids there's loads of things to do. Waterparks - aquaventure at Atlantis and wild wadi (but I think wild wadi might be closed for maintenance at some point soon). kidzania is fun - kids go in on their own through a boarding gate and "work" to get "money" they can then spend! They can be firemen, police, newsreaders, fashion designers, perfume makers, pilots, dentists, doctors, burger flippers - the whole place is a massive pretend zone - mine LOVED it there. Dubai is very kid friendly.
I think it makes a great holiday destination but be prepared to shell out money again and again and again. Nothing comes cheap, not even the genuine fakes!