Why does my mozzarella crumble?
It's a bad recipe.  Here's why:

The way to make mozzarella without using citric acid is to use cheese cultures to acidify the curd, since in order to achieve the cheese's characteristic stretchiness it needs to have a pH of between 5.0 and 5.6..

That recipe has you add a "culture":


  Add 1tsp natural yoghurt for each liter of milk (I doubled this)


... however, yogurt is not the same as Thermophilic cheese culture, which is what you use in mozzarella recipes. In fact, the 40C temperature you used is enough to kill the yogurt culture, meaning that it likely didn't acidify the milk at all. Besides which, the yogurt culture would have had other, undesirable, effects on the texture of the curd.

There's lots of other weird and suspicious factors in that recipe (18 hour drain?  WTH?); I'd recommend simply discarding it and using the Ricki Carroll recipe instead.