That his wifey already seemingly being plenty troubled when they arrive at the island goes against that theory. Same for his son not being affected. And they also show that erratic behaviour after having been outside their home for a rather long time, like when he slaps the kid on the cliff or her visiting the clinic. Looks to me like nothing more irregular than a double case of depression and a broken marriage.
Not to downplay depression, of course. Just saying that it needn't be something exotic. When you hear hooves clopping on the plaster, think of horses, not zebras.