An aquatic creature like a small dog makes me immediately think of the pinnipeds- seals and walruses. They're a little big to be small-dog-like, the smallest seals being around a meter long, but that's nothing a little evolution can't handle. At least pinnipeds have fur, unlike cetaceans. As an added bonus, they're in the dog-like half of the order Carnivora (as opposed to the cat-like half), although they're more closely related to bears, weasels, and raccoons than dogs.
Seals have streamlined bodies and flippers, which is a step away from the ahuizotl's grasping forepaws. However, they could be an intermediate evolutionary step. Perhaps a population of raccoons found evolutionary pressure to take to the water and quickly evolved waterproof, seal-like fur, but have yet to lose their dextrous paws.
A very long tail is easy; many carnivorans already have those (although no existing pinnipeds seem to). An extra hand at the end of it is much harder. There's really no reason I can think of for such a thing to evolve. Some animals, such as New World monkeys, already have prehensile tails, with which they can grasp things by wrapping their tails around them. This works well enough, so there's little evolutionary pressure for any more sophisticated hand to evolve and quite a bit of pressure for it not to. Hands are darn complex, and vertebrate tails have exactly none of the support structure required to make them work. Perhaps the ahuizotl has a simple prehensile tail, and the "extra hand" bit is nothing more than a myth. I'll get back to this in a minute.
Mimicking human cries is easy enough. Just gotta have vocal chords that are the right shape. It's not likely that these things would evolve specifically to sound like humans, so we'll write this one off as a coincidence like how some hyena calls sound like human laughter.
Drowning adult humans is... hard. Unless they're already incapacitated. Or drunk. Or can't swim. I am reminded of the evil carp of Dwarf Fortress, which were famous for their ability to provoke unsuspecting dwarves into leaping into rivers to their doom. Most humans, however, aren't stupid enough to leap into a river at the sight of something in the water lashing out at them. Especially if they can't swim.
Anyway, this is where the prehensile tail comes back in. Maybe, instead of simply trying to drown humans, the ahuizotl simultaneously drowns and strangles its prey. The ahuizotl tricks unfortunate humans into falling into deep water, perhaps by grabbing at their feet and tripping them, then wraps its long, prehensile tail around the human's neck. The combination of suddenly being dumped into cold water and having a wet tail cinching down around your neck could well lead to panic and drowning in short order, especially if the victim can't swim. This could even contribute to the "extra hand" myth- to a terrified observer, this could well look like the ahuizotl was wrapping its hands around the victim's neck, much as one human would strangle another.
Selectively eating, digesting, and getting something out of human eyes, nails, and teeth is... weird. Maybe there's some nutrient in those parts that the ahuizotl can't get any other way. But nails are just keratin, a protein found in larger quantities and in a much more accessible form in skin. And teeth are darn near impervious to all kinds of things. Maybe they need to harvest the special photoreceptor proteins from human retinas for some reason. Or maybe human teeth just make good gizzard stones? A bit far-fetched, since I'm having these thing evolve from mammals with their own teeth, but I'm running out of ideas here.
Or maybe those parts just taste good and get eaten first, and every now and then somebody killed by one of these things gets pulled out of the river before the it gets a chance to eat anything else. This could lead people to believe that ahuizotls eat eyes, teeth, and nails, which could eventually morph into a myth that they only eat eyes, teeth, and nails.