Chris, you've posted an awful lot now on this problem and you keep coming up with logistical reasons as to why you're not taking our advice
. I'm sorry to say this, but based on all your previous posts and this one, I'm beginning to get a nagging doubt that your home is the right one for Jess. A number of forum members (including myself) have spent a lot of time suggesting ways of managing the conflicts that keep happening and suggested that you keep Jess and the kids separate other than for supervised play only at the moment. You've chosen not to do that. The kids are getting bitten and Jess is becoming increasingly defensive and stressed - and it's likely that all these incidents will be ingraining her defensive behaviour. It sounds like you are frequently leaving her in situations that are making her very uncomfortable and not supervising her with the kids. She's not going to improve unless you change the way you are doing things. Leaving her alone in 'unsafe' areas of the house where she can steal food (pretty much every dog I know would take food out of open cupboards) and then just telling her to 'leave it' without offering her something more valuable as a swap, will just make her guarding behaviour worse and set back any positive training you are doing with that problem also
She is
only 5 months old and I wouldn't expect a 'leave it' command to be solid until a dog is much much older - particularly where high value possesions are concerned.
Puppies are very very hard work but this is a long term thing - she is so so young still and I really feel you are expecting far too much from her (and the children) at this stage. It's likely you will have to put a lot more careful work into her for at least another year (plus) before she starts to mature and settle. You CAN NOT expect children to help train a young pup or be responsible for her when you're not around, particularly one that is developing behaviour problems through it's environment. Children do not have the life skills, consistency, patience or restraint required to manage a difficult puppy. Children also move and behave in a very different and more unpredictable way than adults which can put dogs and puppies on edge - this could also explain why she has snapped even if the little boy said he didn't do anything, it could just be the way he moves that's putting her on edge. I really don't understand why you continue to leave them unsupervised after everything that's happened? It's extremely irresponsible towards both the children and the puppy.
In my honest opinion you need to change how you are managing her, listen properly to the good advice you are being given - doing building or DIY work on top of everything else at the moment making your house even less puppy friendly is absolutely crazy right now. If you are serious about keeping this puppy and nurturing a wonderful family dog then you have to prioritise managing her and the kids properly until she is a lot lot older and put a lot of time into positive training. Otherwise, I really think you'd be best contacting her breeder or a rescue to help with a re home before she develops further behavioural problems that will make her very difficult to re home
I'm sorry to sound so harsh but I think you're running out of time to start addressing this properly. Unless you accept the size and seriousness of the job you have here I really think it would be best for all of you if you considered finding her a new home.
To give you an idea, my dogs are now 4yrs and 6yrs and my children are 8yrs and 2yrs (but both children have ALWAYS lived around dogs from birth and are very natural with them). I don't have to supervise constantly now for lots of reasons (not least that the dogs are older and have been well managed around kids all their lives) but I still always know where they all are and if I need to nip upstairs for any length of time I still separate them. I've NEVER had a snap, bite or even growl incident with any of my 3 dogs (2 from pup and an older rescue) where the kids are concerned because I've never let it get to a stage where it could happen. My current cocker would definitely have behaved as you are describing Jess if I'd left him loose with kids at that age as he was a nervous puppy and very defensive, but I didn't and he's now very chilled out around them and not at all stressed by any amount of boisterous 8yr old boys or mischievous 2yr olds. The children have had as much 'training' as the dogs and they all know how to ask them nicely for balls/toys etc and praise and reward when they are given them. So my pup who was a serious 'guarder' now gets a lot of pleasure from giving up his loot to any of us
They can also all walk past him when he's eating etc etc where as when he was the same age as Jess, if he was eating and I even walked in the room he'd freeze and growl to warn me away. We were just sensible with him, took the pressure off him and put a lot of hard work into helping him learn to trust us, and enjoy us. I wasn't confident in him around the kids until he was about 2yrs old himself and he's brilliant now
Having said all that, I still wouldn't ever abuse the trust he now has in us or put him in a position where he might feel threatened by the kids.. but that's life with family dogs and kids.