As with any breed, there are some Shichons  out there with bad temperaments.  You do have to be really careful where you get one from.  There are several factors which can affect the temperament of your new Teddy Bear puppy or Shichon puppy  and how it will do with your children

Please remember that Poodles and Bichons are a pretty yappy breed by themselves and can be a bit nippy

Genetics.  For example, if there's been in-breeding in the dog's ancestors, or if there are just a lot of poor quality, unhealthy dogs in the dog's background.  Your best bet to protect yourself is to avoid dogs that come from pet stores, as they mostly come out of puppy mills.... Find a breeder that has been doing this mix breed for many years and has people that can testify to how great their dogs are

The second factor is how the dog was socialized by the breeder.  When looking for a teddy bear puppy or a Shichon make sure that the breeder has children and has been raised around kids. This is the a good way to ensure you will get a Shichon Teddy Bear puppy that will bond with your children and grow up with them

 If the puppies spent the first 8 weeks of their lives in a cage with minimal human contact, you're asking for trouble.  This is exactly what happens to puppies from puppy mills (which is where almost all pet store dogs come from) and from high volume breeders.  If you're buying from a source that almost always has puppies for sale, this should be a red flag.  They have puppies so often, that it's just a business for them.  They are probably not spending a whole lot of time socializing the puppies...  they're cranking out puppies in such volume that they just worry about the basics such as feeding, cleaning, and marketing the dogs.  You'd be much better off to get a puppy from a breeder that only has a few litters a year, and raises the dogs in a family environment where each puppy gets to spend lots of time out of cages and with people.

Finally, another big factor is what you do with the puppy after you buy it.  If the puppy is placed in the wrong kind of situation...  you can ruin the temperament of even the best puppy.  For example, even the best bred Shichon  puppy is going to have some major personality problems if you leave him/her alone all day every day while you go off to work.  Shichons are very people-oriented, and just go crazy if left alone most of the time.  They bark, they chew everything in sight, and they're so glad to see people at the end of the day that they get themselves worked up in to a total tizzy! 

This is a good way to ruin a Shichon puppy and have it not be a good match for your children.