I do not normally approve of children being taken out of school for a holiday, but this one does seem to be a rather special reason.
Do not think that schools these days, have the authority to 'permit it', Totally daft - when my children were small and in primary school, on really good weather days, would take them all out of school to give us the opportunity of having a day's outing to the beach. Always phoned the school early in the morning saying exacrly what I was doing - would never have lied about it.
Did none of them any harm, all have excellent degrees and higher qualifications.
Of course, this would not be allowed these days. About time schools were brought back to being given authority to their own Heads.
I would say the the OP that it sound lovely that this trip is planned and will probably be some excelelnt medicine for their Nan. So worth paying the fine and being done with it.