When this question was discussed in chat with the querant, a couple of days after asking, it transpired that the bearded dragon had died unexpectedly since the question was asked. I've answered the question as though the bearded dragon was still alive, although I have admittedly focused on the kittens.
The problem with telling your housemate to take better care of his pets, is the rather strong implication that he isn't doing so now. If you want to teach him how to take care of his pets, he first has to acknowledge that. Were you not moving in a few weeks, that would be the path to follow.
Take all three kittens with you
Since you are leaving in a couple of weeks and Alice seems to be on your side, you may be able to take all three kittens with you, to take care of them yourself.
This is not a general solution to teaching your housemate to take care of his pets, but it is a solution for the third kitten.
The bearded dragon was already his, there's not much you can do about that.
When you criticise him and tell him he's not properly taking care of his pets, he may perceive that as an attack on him. He'll want to defend by proving you wrong. The only way to prove you wrong, is by keeping the kitten and having that kitten thrive by continuing his current way of taking care of it.
Instead, shift the blame and the reason for taking the third kitten with you to something outside the both of you.
The three kittens are growing up together, it would be cruel for them to be separated.
That leaves him with a way out. He may be aware that he's not taking care of the kitten very well, but may not want to come to terms with that. This way, he will be doing something that benefits the kitten, proving that he is a good pet owner — he loves the kitten so much, he was prepared to let it go.
Also, offer and be prepared to compensate him financially, showing that it's not about you getting a third kitten in some sneaky way.
You could even get them a new kitten, but give it to Alice, if you trust her to take care of it.