All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger.
First of all, may Allaah reward you for feeding this animal, and this is one of the acts of worship by which one gets closer to Allaah. It was proven that Abu Hurayrah narrated that the companions asked the Prophet “Do we get a reward by serving animals (by feeding them, taking care of them and the like)?” He replied, “You get a reward in every living being (animal).” [Al-Bukhari and Muslim]
It does not appear to us from what you mentioned in the question that you were negligent or caused the death of that kitten; rather, we hope that you will be rewarded for your efforts in trying to preserve its life. So you should not worry, and you should not preoccupy yourself by thinking about this matter; rather, you should be concerned about what will benefit you in your religious and worldly affairs. For more benefit, please refer to fatwa 301042.
As regards your saying, “I am wondering whether it would still be alive now if it had stayed with its mother;” the answer is that since Allaah decreed that it would die at a given time, then this would inevitably have happened. Allaah decrees things with some reasons; Allaah decrees that so and so dies due to an illness and so and so by being killed, and so on. So we cannot say: if it had not become sick, would it have died? This question is wrong. What Allaah decrees happens inevitably.
Allaah knows best.