We spent a long time researching the best breed when selecting a small dog for our home. I highly recommend you do as a first step because small dogs can be very, very different in temperament. Our kids were then 4 and 9. I am allergic so also needed one that is nonallergenic. I agree with the other poster about Llasas. I had one as a child and they really are not the most friendly breed. Steer clear. Poodles are highly energetic and frisky and can have temperament quirks. Not all of course but something to watch for. Bichons are generally very sweet dogs (my mom has one) but they have become so popular of late that you need to be careful also about temperament. The white coat is also tough to keep clean (something to consider if bathing them is an issue). No experience with Havanese I'm afraid.
We wound up with Shih Tzu pups. Bought one 9 month old from a breeder and loved her so much we purchased another pup 3 months later (different breeder--actually through a newspaper ad--awesome dog). Now of course everyone loves their dog but for this breed I would say that you have the advantage of a really good natured, sweetie that was bred to be a people person. They don't need much exercise, which is helpful for us because we don't have a fenced yard or time for multiple walks each day. One of my dogs is friskier than the other meaning he likes to chase and retrieve a tennis ball for 15 minutes or so...but then he gets quiet again! They are very gentle with kids. Crave affection and give it back. I keep my dogs very short as their hair grows and grows so a consideration with this type of breed (and others that are non allergenic) is you will have to either learn to use grooming clippers or plan to have them groomed regularly.
If you are interested in a Shih Tzu and can't find one at a shelter or via the other sources mentioned in these postings, there are great breeders around. I would recommend looking for a more energetic Shih Tzu if you go with that breed as they are just a bit more fun for kids than the really quiet ones (which are best for really quiet adults!).
One final thing to be aware of--small dogs are notoriously harder to housetrain. They take longer for some reason -- at least that is what i always heard and it was true for us. Be sure you are ready for this when your new one arrives (and with 4 kids it could be tough!). Adopting an adult might alleviate that concern.
Last but not least..just don't go to a pet store to purchase.
Good luck. I'm sure the new pup will bring tons of love and enjoyment to your home.