Not sure about the schooling issue but we gave ourselves four weeks to find a rental in feb of this year. We managed it but we cut it quite fine and it was quite stressful. There wasn't a huge amount of choice and we got lucky on the one we wanted but a few more weeks would have made it easier. You wil probably find even less choice near the coast. Saying that our fully furnished holiday let was quite grim and depressing and moving into out own place with our own stuff made so much difference to settling in and home sickness.
good luck
