A corgi makes a perfect family pet (adult size is 25-35 lbs). Since they are really a mid/larger sized dog on short legs, they are not yipey like most smaller dogs and due to the size of their body/chest, they have a big dog bark (and the mouth/bite to go along with it) and are very protective of their families. They are great with kids and don't run off as they are herding dogs and they will keep likely almost always stay with your kids when they're outside and typically follow you around inside.
The downside is an undercoat, but there are fluffies which don't have the undercoat. And, due to their short legs, they typically can't jump up on furniture - a good vacuuming once or twice a week takes care of any of the fluff that does shed and weekly brushing keeps it minimal. I have one of each - after losing an adopted corgi last year, so you have all my sympathy for having lost your dog - it is never easy.
The breeder that we got our dogs from is great - she's located in Sanger - Maria Petrak (Blue Moon Corgis) - she shows some of her dogs, but basically sells the puppies to cover costs of caring for all her animals (she also has donkeys and horses). Her dogs are extremely competitively priced - fluffies are $200 less than others because you can't show them. All dogs come with the papers - you'll get those as soon as you have the dog neutered/spayed (obviously, you'll pay more for the puppies that have the best qualities as show animals), so IMHO, it is extremely ethical of her to require the spaying/neutering due to the amount of unwanted pets. Mamas and puppies are kept inside the house and are socialized early on - she also keeps older dogs in the house and will take back the dog at anytime - if the dog has any defect that you discover within the first year or so, you will likely get your money back. But, mine were very, very healthy - even the mama after having had 7 puppies was energetic and happy when she came home with us (I had originally called Maria about getting an older dog and she kept one of the female puppies from the litter for future showing - mama was beautiful but one ear was floppy).
Corgis are very, very social animals and LOVE people. Corgis were rated the best family pet in Family Circle magazine a while back - they need some exercise, but not too much. I walk mine everyday for about a mile and that makes them sleep (and behave) well. Another bonus of corgis is that due to their body size, they have good size bladders and they are very, very smart, so are very, very easy to house train - about 4 weeks for our puppy (ie., fully house trained by the time he was 3 months old).
If you really are determined to avoid the undercoat, a Jack Russell terrier would be good. But, they have a bit more energy than corgis and are a bit more yipey (my preference for smaller animals is cats since they don't bark ;)
Also, I typically encourage folks to contact rescue leagues/shelters (there is a DFW corgi rescue league), but given that we lost our corgi to kidney failue (she was only 7) after having her just over 3 years, we really wanted a dog with a known background/health history so that my kids would have a pet to grow up with. In the future, I do plan on entirely adding to my family of fur children through rescues.