It does sound like your vet subscribes to pack/dominance theory picnic. Sadly not all vets take the trouble to keep up to date with current research.
Hopefully the behaviourist will be more informed. If they do start up with stuff about dominance and pack structure - run a mile. Whilst their methods might temporarily mask the problem, they would be setting up a potential time-bomb as the do will just be controlling the same fears and compulsions and in all likelihood would end up reacting very badly. Why wouldn't they refer you to an APBC member?
I don't agree with the dcs giving him commands while he is behaving like this. In fact I don't think young children should be trying to control dogs - all the advice given to children is that if you need a dog to do something, eg get off the sofa or move out of the way - ask an adult. Getting kids to tell him what to do is asking for trouble, imho.
I don't allow my dcs to command my dogs until they are fully trained and reliable and then not until they have each spent time with me learning how to do it properly. Even then it's just things like, 'sit' and 'wait' before they throw a toy and 'gentle' when taking a treat and only ever under my supervision.
As for you being assertive, if she was up to date on modern training methods, she would understand that it's consistency that matters - assertiveness is essentially just pitting your resolve against theirs and nine times out of ten that is just setting you up for failure. Modern training motivates them to want to do the things we need/want them to do and they learn this is the best way to behave by constant and consistent positive reinforcement.
To be honest, she is not qualified to comment on breed or behaviour - she is a medical doctor for dogs - in most cases, but not all, the equivalent to a GP and certainly not a specialist in canine behaviour - hence the need to refer.
I would have thought the not being happy in himself is quite possibly down to the digestive problems. Did she not consider that?
Sorry it was such a horrible consultation. Fingers crossed the behaviourist will know their stuff and soon have you and Legend on the right track.