Praise be to Allaah.
Allaah has enjoined kindness in all things, as it says in the hadeeth: Allaah is Kind and He loves kindness in all things. Narrated by al-Bukhaari (5678) and Muslim (2165).
Muslim (2592) narrated that Jareer (may Allaah be pleased with him) said: I heard the Prophet (peace and blessings of Allaah be upon him) say: Whoever is deprived of kindness is deprived of goodness.
Remember that whoever has any kind of animals must protect them and give them food and water. It is not permissible for him to expose them to danger. In the hadeeth that you referred to, the Messenger (peace and blessings of Allaah be upon him) told us that a woman entered Hell because of a cat that she detained and did not feed it or let it eat from the vermin of the earth, i.e., insects. Narrated by al-Bukhaari (2365) and Muslim (904).
It was narrated that Abd-Allaah ibn Mas'ood (may Allaah be pleased with him) said: We were with the Messenger of Allaah (peace and blessings of Allaah be upon him) on a journey, and he went to relieve himself. We saw a bird with two chicks and we took away her chicks, and the bird started flapping her wings. The Prophet (peace and blessings of Allaah be upon him) came and said: Who has upset this bird by taking her children? Give her children back to her. Narrated by Abu Dawood (2675); classed as saheeh by Shaykh al-Albaani in Saheeh Abi Dawood.
The point is that whomever Allaah has given any of these animals to look after, such as if they are in his care or he is raising them and keeping them for some need, then he must look after them and treat them kindly.
Based on that, then you have to repent to Allaah for several reasons:
1 - Disobeying your parents whom Allaah has commanded you to honour and obey so long as there is no sin involved in doing so.
2 - These kittens were in your care but you failed to look after them, and that led to their death.
3 - You upset their mother by separating her and her children, then her little ones died.
Undoubtedly the feelings of sin that you describe indicate that your heart is alive and that you have sincere feelings of regret for what you have done.
But perhaps that has gone too far, such that you feel despair, and this undoubtedly is not permissible, as Allaah says (interpretation of the meaning):
Say: O Ibaadi (My slaves) who have transgressed against themselves (by committing evil deeds and sins)! Despair not of the Mercy of Allaah, verily, Allaah forgives all sins. Truly, He is Oft‑Forgiving, Most Merciful
What about the vastness of Allaah's mercy, which encompasses all things? What about Allaah's acceptance of His slaves' repentance, even from major sins?
The Prophet (peace and blessings of Allaah be upon him) told us of a man who killed ninety-nine people, then he killed a devoted worshipper, thus completing one hundred, then he repented sincerely and Allaah accepted his repentance - as is narrated in al-Saheehayn. What is your sin in comparison to his? He killed one hundred people then repented, and Allaah accepted his repentance. So you have no right to despair of the forgiveness and mercy of Allaah. Do righteous deeds and always remember the words of Allaah , may He be exalted: Verily, the good deeds remove the evil deeds [Hood 11:114].
And Allaah knows best.