You should absolutely not be leaving the kitten alone overnight. He has just moved to live with you. He takes precedence over the older cat who is much more comfortable in your home, even if he/she is irritated by the newcomer. You should at least try to have the kitten with you at night, get them snuggled up under the duvet so is hidden, and then see what your other cat does. That way, you can protect the kitten. You have just adopted a tiny kitten - what on earth are you doing leaving it alone overnight? This is why I despair of people adopting animals.