Housing in ALA is on the higher end but you should be able to find somethng at that price including all your utilities. Much would depend on where you want to live and how big a space you're willing to tolerate.
If your kids are really little you can get by with local daycare/kindergarten, which isn't too expensive. If they are more school age, then, yes, international schools run a little over $10K/year so times x2 with a discount, you're probably looking at $18K just for schooling. That alone will eat about half of your $3K monthly income.
If you're looking at LOTS of kartoshkas (potatoes) and sitting at home watching TV or you plan on leaving the family in their home country while you come out, it doesn't sound like that great a deal.
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