DROGHEDA, Ireland — Moving to a newly built seaside housing development north of Dublin seemed an obvious decision for Katrina Dooley and her partner. Fast-rising property prices in the center of the city allowed them to trade their one-bedroom apartment for a three-bedroom, red-brick house in Laytown, a coastal enclave near here, within earshot of crashing waves. Central to the couple’s calculation was being able to concentrate energy and attention on their child, Ella, 5. The problem was that hundreds of other people had the same idea, leaving a local school scrambling for space, to the point of using a...