It’s probably for DBS / safeguarding reasons. When applying for roles in schools you have to give a full employment history and explain any gaps. It’s not to judge or invade your privacy, but to check you weren’t in prison, not omitting a job from your cv, etc.
OP had (presumably) already told them she had been a SAHM. Which do you suppose is more likely: that she'd been banged up in jail, moonlighting, running a drugs cartel etc.... or, erm, looking after her children, whose existence is easily provable? Being a married SAHP is hardly unusual.
This is truly nasty. I get when mortgage and other lenders want to see proof of your income, as this is relevant to your relationship with them. As for employment, unless you're seeking to be a very high-ranking (and very well-paid) civil servant/government department leader or similar, why on earth do they need to know what you were doing for employment before you worked for them? For a highly-valuable much much under-paid TA? Of course, the DBS is a requirement, but checking if you've got/had a criminal record is miles apart from demanding to know how your family manage their finances.
If you don't need the job (or at least them), I'd be so tempted to send them an explanation letter saying "When a man and lady love each other very much, they have a special cuddle and sometimes this results in a baby, which then has to be looked after for a number of years. This might be surprising news to you, but it is in fact, normal - and if this didn't happen, humans would actually soon die out. In fact, YOU yourself were once a baby and had to be looked after by a grown-up (this was probably mainly done by a lady)."
Seriously, the very thought that somebody wanting to work with children might also actually be one of those not-very-rare people who wanted to have children of their own.
Otherwise, I'd give them and their practices some SM exposure. This is outrageous and it IS sex discrimination. They may say that they would ask a male applicant for his wife's bank statements (and I wonder if they actually would do this in practice), but just because SAHPs can be either sex, the vast majority are women, ergo it's clear sexism.
Considering that the DBS is already in place specifically for this purpose, they're effectively suggesting that anybody who has taken time out of work to look after children (mainly women) needs to prove that they're not a criminal; whereas those who haven't (mainly men) - who could have had any kind of illegal side-hustle or embezzlement scheme going on as well - are vanishingly unlikely to be criminals. Paid employment is for honest, decent people; looking after children is for shady, untrustworthy probable-criminals. They really need to be called out and exposed publicly for this and made to justify their sexist, discriminatory actions.