Try small rescues in your area - do a google search and you'll find lots. They are often more flexible about children (although yours are over 5 which is usually the minimum age).
I know loads of people love Labrador/retriever types, but I personally wouldn't go for one. They are big and chunky, grow to a large size, need lots of exercise. A friend of mine has one, she wasn't really into getting a dog but was pestered/blackmailed by her husband/kids. The retriever is lovely but too strong on the lead for the kids to handle, too strong for HER and they just haven't put the time in to train her to be good on the lead.
I've noticed a lot of men want a big, manly dog but it really isn't so practical when it's often the lady of the house and the kids who are doing the majority of the looking after, walking, training etc. The smaller size dog does make a difference. They also take up less room overall, are easier to get in a car, eat less food, do smaller poos! They are not just toy/lapdogs, they have plenty of personality and va va voom!
I would look at a lot of different rescue centres. They will not only have "difficult" dogs, but they often have puppies from unwanted litters, from people who have had to move into rented and can't have a dog etc. Also, a lot of rescues use a foster system for their dogs so dogs have been assessed in a home environment, often with kids, cats, horses or even ducks! Good luck 