Join the FB page for black retriever X rescue - lurk and see how they operate. They are fab. I've supported them for years. They do get dogs that are used to children and they are scrupulous about matching dog to home - AND they give follow up support if needed.
I've had both pups and older rescues with young children. It's doable with the right dog - I had one that didn't work out (direct Rehoming from a friend of a work colleague) basically they had lied and minimised the dog's issues - he injured my elderly cat who had to be PTS
. It was a hard lesson to learn. I've had three other dogs that came direct from original owner (one via breeder taking back a dog, one via breed rescue and one I knew personally locally) also two from RSPCA. I've also had pups when the kids were little.
As you might guess, I'm not the House proud type, your children have to learn to shut doors, baby gates etc. And put toys, shoes, school bags, away. Even with an adult dog, hide the TV remotes.
I had dogs before children, so felt pretty confident about dealing with new dogs around children. I know you are used to dogs, but the full time dynamic can be different. I would advise taking your time and doing your homework, because if it doesn't work out it's traumatic for everyone, my kids were 6-9 when we had our failed rescue and they very much remember it (now adults ) one in particular loved that dog but I couldn't risk it, he was huge, powerful and out of control ☹️
Having said that, the two from the RSPCA, where we had no history, have been wonderful little dogs, but with some issues (the RSPCA staff get to know them so take what they say seriously). My current RSPCA mutt was returned to them after his first weekend with his initial adopter - he had a fight with her sister's dog. He loved my elderly retriever, and adores my new young one, but yes, he is reactive with un neutered males and can't be let off lead. OTOH he's fine with the cats, loves children and is a dream in the house. You might want to think about what behaviours you really don't think you could cope with, be honest with the rescues about your lifestyle etc and good luck.