The references to 'things being done differently' in Saudi Arabia and the Philippines are complete red herrings.
The moment the nanny enters Spain, she becomes subject to Spanish and EU labour laws on working hours, breaks, minimum wage, and safe accommodation.
A blow-up bed in a study is not legal accommodation for an employee in Spain or most of Europe. Employment contracts require reasonable and private housing.
Putting the nanny in a non-private room compromises her right to rest and privacy, which is a legal breach.
This accommodation is objectively exploitative, regardless of the nanny's personal opinion or traditional customs.
The type of visa the nanny uses to enter Spain must be compliant with the work she is performing. If she is performing work as a private domestic employee in Spain without the correct Spanish work authorisation, the employers are employing an undocumented worker and forcing her to violate the terms of her entry.
Of course if she were to take part on the holiday as a holiday and perk of her job, that is absolutely fine - but she must be on holiday and absolutely not taking care of any children, cooking meals or helping out in any way that could be interpreted as work. (All other adults would of course be expected to pitch in domestically, but then their relationships with each other are family-based or friendship-based, not employer-employee based - the holiday isn't a perk of their job.)
In other words, if she is entering only as a travelling family member and not working, then she should not be doing any childcare.
Even if the visa were correct, if there were any expectation of one nanny to look after all the children of a multi-family group for a week, this would go far beyond the normal terms of a single domestic contract - massive scope creep that requires a new contract, clear limits, and drastically increased pay. It is exploitative to expect an exponential increase in workload without commensurate compensation and contractual change.
Denial of autonomy is not infantilising or 'saviourism'. The concern is not that the nanny should be offended, but that the power dynamic prevents her from safely expressing unhappiness or refusal, or requesting a renegotiation of her contract, especially if she relies on the employer for her visa and housing.
Simply 'paying her for that work' would be insufficient. Even if the visa permitted it, wages must meet the Spanish minimum wage with reasonable time off, minimum rest periods and maximum working hours.
The bigger point is legal risk and human rights violation, rather than personal feelings, expectations or local customs in Saudi Arabia or South Easy Asia. The OP's instincts are right. This situation raises ethical and legal red flags.