"The children have already suffered an upheaval at home and now she thinks bringing them to a different place entirely will be a good move....for her presumably, what about them?"
The children should be the priority. Presumably they were born in NZ? Both under 7?
Whilst I believe the children would adapt to living in the UK quickly, they would miss their friends (at first, anyway) and they would miss contact with their father. Whether they are in NZ or UK, their mother seems to be the resident parent, and her happiness and mental health will have a large affect on their happiness and development.
The problem, in my opinion, is why the mother is desperate to return to the UK - because she sees it as a solution to her problem of depression. Her depression may partially spring from her isolation from her family, old friends, general support network - it's not uncommon for people who emigrate to feel homesick and isolated. That you son can prevent her from bringing the children back to the UK (and I believe he can) must make her feel helpless, which could only increase her depression and make her focus even more on 'coming home' being the solution.
However, returning to the UK is probably not going to be the solution. I have seen at first hand the rootlessness that emigration can bring. When they were over there, they were homesick and wanted to come back. Happy for three months, then missing over there. This played out a couple of times, back and forth.
Would it be possible for her to come for a longish holiday? If the children are young enough it won't interfere with their schooling. She could then see that the UK is not the answer. If she doesn't actually get on with her parents, the realisation might not actually take very long. All her old friends will have moved on, she'll probably feel as isolated here as she does there . And with the prohibitive cost of housing, could she even afford it? If she's not close to her parents, living with them would quickly become horrendous. Moving out from them would need a job, deposits - the practicalities could be insurmountable. Which will do her depression no good at all.
Of course this could all be very expensive, and if her parents are domineering they might be able to make her feel unable to leave again, uproot the children again.
So, ideally - your DIL and son have to TALK. Talk about her depression, isolation, what actually moving back to the UK would really mean. Deal with her depression-fuelled rose-tinted glasses of life back 'home'. Emphasise that the UK and everyone in it has moved on since she left. She would not be coming back to what she left - she might not feel she belonged any more, and then what?