Also it's the time your dog is out off lead that matters, not how far you walk in that time. When my son was born we had a springer spaniel (very high energy), so once my son wanted to be toddling around I either walked with him in a buggy to an off-lead area, or drove there and then the dog could race around while my son toddled and I played with both of them. My son just grew up knowing that walking the dog was part of our daily life.
I think one of the best things you can do for your kids is give them a dog to grow up with. It teaches them responsibility, how to care for another being, respect for animals, discipline and so many more things. A puppy is going to be overwhelming for anyone no matter what, even if it's the 10th dog they've ever had. But if you have the time and dedication to learn about raising it and learn together with your puppy as it grows, you should be fine. Your kids are going to learn some great values growing up with a dog, and the love it's going to bring into your family is incomparable!! It's unlike anything else. Congrats to you and your family!
I just got a working lab soon 4 weeks ago (she was the biggest one in the litter) and I got a 2 1/2 year old daughter. Best decision I ever made. My daughter already knows how to play nice with Millie and how to throw a tennis ball (my daughter holds the ball and say sit and then throws it). Then if Millie comes back my daughter say let go and try get the ball out (Millie lets her and don't bite or nibble). We did have a 3 day period of Millie nibbling her a lot but I did not interfere unless it got out of hand, when Millie nibbled her my daughter would scream which made Millie back off (if she didn't I put her in the crate for 30seconds and then repeat it). Now just a few weeks later we barely got any kind of any nibbling and they both play hard together and nap together on the sofa.
I was in the same boat as you when we got our first Labrador. Our children were 10, 8, 7, and 2,5 years of age. The dog was a blessing in many ways. Our youngest didn't get too much attention anymore. All the attention went to the dog. We learned our lab that family comes first, then nothing and then she... When the children got older we could walk the dog in the evening and talked with each other about important things, without the children who were not asleep just yet and their big ears couldn't hear what we were talking about. Our little girl used to play with the dog in the garden. When she had chalk we had a rainbow lab instead of a yellow one. For us she was a great blessing and joy, I think you won't regret it. You have to raise the lab together with the family. All has to be consistent with the dog. It helps you also with the upbringing of your children....
I forgot to mention that it's not until I can tell on my daughters scream that it really hurts I interfere. All 3 of us takes a 15 min walk in the morning and in the evening my husband comes along. I introduced the stroller day 2 we had her with having the stroller first just standing in the yard near where we were, then I pushed it once in a while so Millie could see it moves. Then next day I put my daughter in it and pushed it in the yard so that she got used to it having someone in it. Day 3 we had a successful walk without her trying to bite the wheels or being scared of it (I did not have her on a leash in the yard so that she could choose herself when to approach).
Since I mentioned earlier about my 2 sweethearts napping together I took a picture now when my daughter is about to pass out with Millie. You should just worry about getting the future pup opportunities to improve and praise him/her for doing so. And get some good chew toys that won't be eaten up in seconds. I got 1 big gummy kind of thing with wobbly dots on it that my puppy loves along with 2 smaller chew bone alike things (can't figure out the name at the moment of them). Tennis balls is a must. We don't got that many toys yet but she's happy with what she got for the moment plus she hasn't stolen my daughters toys or chews on anything else (sure that will change its too good to be true).
I have a lab from working lines, she will be 1 on Sunday. My daughters were 4 and 6 when we brought our Buffy home. I won't lie, there were times when everyone was in tears and saying we would send her back. Puppy teeth are SHARP and it didn't matter how many times I told my girls to stand still and stop squealing, they would run around shrieking while Buffy ran around attacking feet. This might sound like an odd tip, but get dull coloured shoes and socks for your children. Buffy seemed to go for bright colours much more, maybe because her toys are brightly coloured. I'd also make sure there is a way to separate the children and puppy, whether it's a different room or a puppy pen. They will need a break from each other. Make sure you get several Kongs so you've always got one ready in the freezer. When your pup has a 'zoomie', a stuffed Kong is a brilliant way to get them to sit still and calm down. There are some good videos on youtube to show kids how to read dog body language so that they will know when to leave the puppy alone. Obviously you need to make sure they are supervised when they are together so that no one gets hurt. Buffy is our first dog so I've no comparison to show lines, but she definitely enjoys having a 'job'. She loves to swim more than anything and I can wear her out doing water retrieves while the girls sit and watch or take turns throwing the ball, so there's not necessarily long walks involved every day. I'm also going to start canicross with her in a few more months when the weather has cooled off and she's a little bit older. Would I do it all again?..... Absolutely. Although that would definitely be a mad thing to do! But she is calming down a lot and it is lovely to watch my youngest snuggling up to her on the sofa and saying "I love you, Buffy." And Buffy is absolutely crazy about the girls, she misses them like mad when they're out.