Redundancy from school

Given you're only employed on a 39 week contract to exclude payment during school holidays I would have thought that the 12 week notice would not include holidays, however the problem is that some of your redundancy period would fall into a holiday period.
That will be why there is a dispute. If you're employed in a council-run school their HR should be able to sort this. If it's an academy, however, who knows?
12 weeks notice should mean 12 weeks pay (not 11 weeks pay plus an unpaid week for school holiday which might be half term or two weeks at Christmas). Is that what your HR dept says you'll get?