To me , moving to Australia be it for 5 years or permanently, is a huge decision and has to be one where both partners are on board, bit like whether one partner wants another child and the other doesn't. I don't blame OP not wanting to go there, I wouldn't want to. I couldn't imagine being so far away from family, I certainly couldn't go now, as my elderly DM has moved closer to us since DF died last year. But even before then I would have struggled, and I didn't see my parents as regularly as OP currently does.
OP is not indifferent to her DH's stress, but the feeling I get is that if they go to Australia DH's stress may reduce (though no guarantees the same issues that apply at his current job won't be there at his new job, the grass is not always greener) but the OP's will increase, so they won't be better off as a partnership.
Not everyone likes sun and beaches. Where we live people tend to be split between surfers and walkers, we as a family are most definitely on the side of walkers. DH also grumbles as soon as the temperature gets to a certain level.
I think OP and her DH need to sit down and see what can be done to improve DH's position. Also try and work out what the next step would be if they did go to Australia, are there any guarantees that DH would be able to get any jobs in his niche industry once the Australian contract had finished? If there is no guarantee, would it be a good idea to see if he could branch out anyway. It appears from the OP that he wasn't always in this niche industry, so it might not mean he has to retrain.
Another consideration for me would be that if they do go for 5 years, their oldest child would then be in the secondary school system, and would that be more problematic when they return to the UK?
I also get the impression that DH has always relied on OP to provide/organise childcare when he travels abroad with his job, and all the long hours he does (OP says he rarely gets home for bedtime) If the long hours and travelling still has to continue if he goes to Australia, I assume he will still be expecting OP to do this, so I assume this may impact her choice of work she could do, especially as she doesn't have the same support network as she currently does.