Returning after three days also doesn’t teach resilience, respect and patience to the children, it sounds as though the oldest child is doing well, nothing wrong with working through these early days, do you usually give up on animals with such ease when these could very well work out for the family and the dog
The OP states the dog on seeing the children does a 'Short growl then short sharp loud barks' and that it appears threatened and stressed when they are doing nothing at all, just being present.
That is not a simple training problem, that is a fear aggressive dog and it is a problem that has the potential to get very dangerous in a short space of time.
I am quite sure that if we were talking about a far bigger dog which the potential to do far greater damage it probably wouldn't even be being discussed, it would already be back.
Just because it is a small Shih tzu doesn't mean it can't do serious injury.
The OP states the children are already becoming frightened of it.
A lot of dogs are not comfortable around children and the dog shouldn't be forced to stay in a situation where it is so frightened it actually feels the need to growl and bark at the mere presence of the scary thing.
Its all very well talking about resilience, not giving up etc but what happens if the dog actually does escalate and bite?
Which if not dealt with quickly and correctly it absolutely will...
Fear aggression doesn't just disappear, it gets worse without intervention.
If it does bite, most rescues will not rehome a biting dog.
Most likely it will end up being PTS.
The whole situation is all shades of wrong for everyone concerned.