There should be close to zero play, sounds like you need one or two new axle shafts. Luckily they're not horribly expensive if you can find a used one. I think they go for about $90-100 USD, although shipping to the Netherlands will probably make it a bit more expensive. If you didn't have any lateral motion and just the vibration you could get away with swapping the inner cups, or replacing them, but this sounds like a bigger issue.