@redboxer321 has given some excellent advice and @SpanielsGalore is right about show/working lines. There's also show-gundog (SGWC - the dog will have this acronym by it's name) which are often higher-strung and more energetic. SGWC dogs are 'show line' dogs that have proven their ability to 'work' which is why they tend to be more energetic.
I've linked an example above of what you should be looking for (what I consider a 'good standard') of health tests for a pedigree Golden Retriever. Dam should have similarly good results. If they don't, walk away. They should also have heart tests done (it's not recommended, but there is an increasing risk with the breed and good breeders have been testing for it for years).
I would also add, be wary of the breeder. Obviously you haven't linked them, so I can't say if they're good or not...but there are quite a few litters up on Champ Dogs atm that have all the hallmarks of bad breeding and puppy farming. Mum should not be having a litter before she is 3 and not after she is 6. She should not have more than two litters in a lifetime. The breeder should not have more than a single litter at any given time.
Onto Golden Retrievers more broadly, personally I don't think they're suitable for families with young children. They don't just mouth - they bite, and they lunge, and it can look incredibly vicious and it will hurt because Golden's are like that. There's never any malice, but they are vicious little gits. But that's not the main problem...the main problem is that by 6 months old they can easily be 20kg and still doing that behaviour because they are so slow to develop. Everyone says 'oh it's fine, it's only a puppy' but when that puppy is 20KG and lunging towards you to play with it's teeth bared...people are less happy. And it is always play, but people don't realise that and children don't either.
Golden's are essentially puppies until about 4(ish) and then suddenly they grow up overnight. They are also prone to some pretty unpleasant behavioural issues including resource guarding, separation anxiety and over-excitability (the 'wank gene'). All of them can easily be managed and or avoided by consistent training - but that's where children come in. Children wind up dogs and make everything much harder than it needs to be.
If you do press ahead, which I imagine you will, please remind your children that Golden Retrievers are not toys. That tormenting them will end in a bite. These dogs are far too sensitive to respond well to being bothered. And I spend far too much time helping to re-home Golden's who have bitten young children, or who's family cannot cope with them because they failed to do basic training, and it's soul-destroying to see dogs being failed by the owners simply because their owner got the breed based off you-tube videos of Emma and Ellie, or Teddy or Tucker and Todd. Golden's are absolutely lovely dogs, but they are not as easy as social media makes out and they are not just 'fluffy labradors' (as someone once said to me)!
If you're willing to put in the work, and have very clear boundaries with your children about the dogs, then go ahead. And if there's anything I missed, very happy to answer any questions 😊
Finally, please remember: breeding is a huge part of what makes a dog healthy - you can fuck up a well-bred dog, but you can't un-fuck a badly bred one.
Just to add to previous posters and a bit of misguided 'help' they have offered;
1.Mongrels are not automatically healthier. What makes a dog healthy is the health of it's parents and it's relative COI. All dogs being used for breeding should be fully health tested. For Golden's this is; hips, elbows, DNA PRA-1, DNA PRA-2, DNA ICT-A, ISDS. Just because you breed two dogs of different breeds, does not mean thay re healthier, particularly given so many breeds have such serious (and similar) health issues. Poodles and Goldens, for example, both have hip, elbow and eye issues along with heart issues. If one of those parents has a bad 'score' then chances are the offspring will as well. My own dogs are extensively tested - my oldest girl is 14, still capable of doing 3 mile walks twice a day. THAT is what a healthy pedigree dog is capable of.
The photos PP have linked actually just show how the 'show' world has changed - you can easily tell the dogs structure has not changed that much, simply the position of how the dog is made to stand to show off it's attributes. The 1950 dog is almost exactly the same as the 1990 dog (and the 2000 dog is just impossible to actually see...), it's just the way they are standing and angle of the camera that is different.
2.Golden's do not steal food when they are properly trained and they also do not raid the bin. They do not have the 'gene' (like labs do) that makes them act like that. It's simply a matter of training.