That is really annoying to have noise this late. Any idea if neighbour below you also have kids? The reason i ask is because, i used to hear running noise and door slamming. But i stay at the highest floor, nobody lives ontop.. err... cant be "something ghostly" ... hee..
Dont waste money on soundproofing. perhaps, you can try to talk to them again. if really cant take it, you can try calling town council (of course, that is not very nice ).