Vancouver is fairly spread out, since its suburbs are often addressed as Vancouver too. The 1400 figure is quite realistic, but you could find something cheaper if you stay out of the downtown core. Burnaby is a little cheaper, and still quite accessible. Surrey is considerably cheaper, bit too far from the town for my taste though, and not a particularly pleasant place to live. If you go as far as Port Coquitlam and such, you could probably make your rent considerably cheaper. It`s not easy to find a place to live in Vancouver though, so I suggest looking up long stay rates at hotels before moving. You`ll need a place to crush while searching for your permanent address.
All that said, how much you need per month really boils down to your own living standards. I think 3000 a month for a couple with two children kind of makes sense. One thing nobody else touched on is smoking. Do you guys smoke? Because doing so will not only make it harder to find a place to live, but will increase your costs dramatically.
Transportation would cost you about 250-300 a month, assuming you`re only using public transit. Broadband internet, home phone and cell phone can each be estimated at $50 or so a month. Could be more, but not really less. Electricity depends on your living arrangement. In a single bedroom apartment it`ll be under $100 a month. So you can assume $500 a month will pay for your utilities each month, or come really close. The rest is food, and we can`t really tell you how much it`ll cost you without knowing what you eat. If you`re not looking for special vegan meals and stuff like that, I`d say 1000 a month would feed a family of four without going to extremes. You`ll probably find cheese very expensive in Canada, and you`ll also find that prices differences between grocery stores can be rather prominent. You should always check flyers and organize yourself such that you won`t end up paying more for the same thing when you don`t have to.