There are a few things here that don't stack up. If the children are too small to eg walk themselves to school, then of course they can't be looked after by someone in extreme psychological distress. So whoever is looking after them needs to come and look after them in their own home where they can be taken to school by the babysitter. If the babysitter cannot do that because they have commitments of their own, like going to work, then they can't look after children who are too young to look after themselves no matter where this takes place.
Two weeks is a lot of school to miss, and in this situation (I'm assuming reasonable financial resources with a job that requires the parent to be away for weeks at a time) an emergency nanny or similar is more appropriate than taking the children out of school for such a long time. Why has this possibility not been explored?
Why is the other parent in such distress that they cannot walk the kids to school and collect them, and why has nothing been put in place before this (childminder, emergency nanny, whatever) before this emergency happened?
Why can't the babysitter stay with the children in their own home where they can keep to a familiar routine, which would be of benefit with one parent absent and the other apparently unable to look after anyone possibly including themselves?
Why is the parent going away for work seemingly so out of touch with the situation that this has arisen as an emergency? Even parents who are away keep in touch with their kids and the other partner at home, and I have personal experience of this.
How old are the kids? If early primary as it sounds, does this mean they've been at home with someone unable to look after them for several weeks already?
I don't think any of this sounds OK on any level. Taking a child out of school for a holiday is very different from carting them two hours away because one of their parents is absent and the other unable to look after them.
I feel very sorry for these children, who seem to have no reliable carers and nobody looking out for their welfare on a daily basis.