Most if not all waxes are pretty easily effected by moisture of almost any kind. However, I think you'll find the main problem here is damage to the Organoil (which in many instances marks and damages easier than wax) this would account for much of the opaqueness and the raised section of timber. An invisible repair may be hard to affect without redoing the entire top.
You really need many coats of wax before you will have any chance of stopping this kind of damage happening. Personally I wouldn't use wax on any kind of furniture etc that was for use with children, becaues of sticky fingers, wet bums, dribble, baby bottles, water and formula spills, paint spills, and all things wet and kiddish, not to mention mothers milk (sorry, had to mention it). There are plenty of infinitely more durable surfaces and none of them are wax or most oils (including organoils)
Cheers - Neil :)