I think there is little doubt that your lens is faulty and needs recalibration or whatever they do. My inclination would be to simply return it and get a new one from the shop.
I'd suggest though that the two examples you posted are not the best way of convincing the camera shop (if they needed such) that there is a problem with the lens; they are both the sort of shot that I remember older cameras' autofocus systems would simply hunt and hunt and I'd end up focussing manually - but first I'd try getting an edge focus and that would often help. Of course you're quite right, often it would lock on completely the wrong thing. It's a credit to the manufacturers that autofocus has improved to the point now where it hardly ever gets it wrong.
Of course how you could convince a squirrel to sit still long enough for all that is another story. I do remember in the early days of autofocus that wildlife photographers found it pretty much impossible to use. Birds in particular proved persistently fuzzy, and there was a great deal of sitting in hides, pre-focussing and setting food "traps" or whatever and tripping the shutter as the animal got to the right spot.