To the OP, I would agree that if you're seriously concerned, it might be worth contacting a behaviourist.
I've had one pup that did resource guard and was difficult for most of his first year and one pup that was a lot less likely to do it and never really a problem. I have young children too and my experience is that all puppies are different (not good or bad) you can apply more heavy handed training methods to some pups without them starting to react, and with others (that still grow into very wonderful adult dogs) you can't do this with without stressing the pup so much that they actually become worse and a lot more unpredictable.
When I got my first pup (over 10 years ago) I was pregnant and before I knew more, lots of well wishers told me it was important to be able to take anything away from him (just take it, not ask him for it) and stick my hand in his dinner so he knew who was in charge etc etc. There didn't seem to be any need for me to do this but although he wasn't keen on that sort of thing, I tried it and he seemed ok with it - probably similar to Seaanglers Peggy.... the reality was, that he was the softest dog I've ever met and would have put up with anything. Fortunately I stopped listening to well wishers and did a lot more research on training and learnt more about how to get the best out of your pup in a much better way. Which is lucky as the next pup guarded everything ferociously and couldn't even take 'no' let alone having things taken from him or his dinner messed around with.
I have young children too and aside timing him out as a pup when we needed to, we have other simple rules that really help... I never EVER give them treats/bones when the kids are around. Children are unpredictable and can make dogs feel uneasy - if they are even a bit worried about their resource they are much more likely to warn children than adults - so for now, don't give the dog things he really values when the kids are around. Move his bed to somewhere he can feel really safe and have a rule that the kids need to leave him well alone when he's in there. When he's eating, leave him well alone for now and give him space so he can relax. I'd then suggest an adult (with no kids around) starts to try handfeeding and then adding food to his bowl while he's eating when he's relaxed enough and eventually when he's relaxed with that, getting the children to do similar. Teaching 'swapping' with the children is a great idea - dog has a toy and you offer something seriously tasty as a swap that's even more valuable and gradually introduce a command with it - long term, the dog learns to happily give up the toy and welcomes you near him when he has it etc as you're associated with a good thing for him. You can start to apply this to more valuable things with him once he gets the idea etc...
None of this is being soft or avoiding the issue - you are simply helping your pup to learn to relax in his own time and trust you all and in my mind, that's a much safer bet than going head to head with a pup and forcing issues. As adult dogs, both my pups have been absolutely wonderful with children (despite serious worries about the second one when he was younger
) and whilst I still don't give them bones or chews when the kids are around (although I could easily do that with my weim) there is nothing else that's a problem.
Dave (was devil puppy cocker) is still a little prone to guarding or stealing things and burying them but the children just have to ask him to 'leave it' now and he happily gives his prize up for a big cuddle or something tasty from them
Had he been handled in a different way in the early days, I FIRMLY believe Dave would have been an unpredictable adult dog which would have been very difficult to manage with young children whereas the first pup probably would have tolerated bad handling and training and still been lovely.
Try not to loose heart, just sit down and try and work out what's triggering the barking and remove/change those situations, then start working on building his trust and letting him learn to relax by practicing some of the positive things I and others have mentioned
