People on mumsnet are crazy when someone mentions getting a puppy, it's not as big of a deal as people make it out to be and people have been getting dogs for their kids for a century now. The puppy gate keeping is really strange.
OP the puppy is going to chase them alot, it's cute at first and then they'll start biting when they chase. Make sure you have a rope toy on hand for your kids to give to the puppy to chase when this happens. Whenever a puppy is biting, tell them "no" and give them a toy to play with instead. I've never had a problem with puppy biting for longer than 2 weeks because they're not allowed to.
Consider using a pen attached to the crate for when you want to bathe the kids/do something in another room while toilet training, they cry less in a pen than a crate. We only use crates at night time to keep them off cables. If your puppy suddenly turns into a demon, it's probably tired and should be put away and ignored so he can snooze it off. Kongs and antlers are great to get a dog to settle when they're in the crazy puppy stage and due a sleep, chewing releases endorphins and settles them down.
Learn how to train a puppy ie the body cues that help with alot of commands, pre train the puppy on how to do it (at that age they'll learn easy tricks in less than 10 repetitions) then get your kids to do it and they'll feel like the puppy extra loves them when it does the command easily. Then remember when he's had his injections, if he tries to sit/play with the leash/lay down on the pavement, be cheerful and keep him moving rather than letting him do it and save yourself a headache when he's doing it at 6 months. Don't let your kids hand feed him human food even if it's adorable, he's a lab and you'll regret it when hes 40kg and pushy with an autistic child eating their food.
Last thing - when toilet training, act like he just did the best thing in the world even if it's to an embarassing extent and give him food straight away for a pee or a poo so he doesn't end up sitting outside for 30 mins when you REALLY want him to go. We crate/pen for the first month unless playing outside/walking (perfect time of year to spend alot of time outside with him) while toilet training so it has a better grasp on what you expect. Our 6 month old toy breed (notorious house pissers) is toileting perfectly using this method.
Enjoy your puppy OP, when you want to pull your hair out remember it's not permanent! Every month they become better if you do the bare minimum, so I'm sure a dog with the breeding you chose and the fact you're seeking out information will be a great friend for your family.