Praise be to Allah.
You did well to complain about your uncle to your father. It was a wise move that is indicative of wisdom, good character and religious commitment. We ask Allaah to give your more of His bounty and to protect you. But you should not hasten to pass judgement on your father and hate him, or doubt his keenness to protect you and take care of you.
Yes, he should be more firm with his brother who molested you several times. The least that he should do is not let him stay overnight in your house and trust him with his house, family and honour. Rather he should not let him visit you and see you. The gheerah (protective jealousy) that is prescribed in sharee’ah means that he should threaten to sever ties with him, because children are a trust that is given to their father, and he is responsible for protecting and taking care of this trust.
It was narrated from Ibn ‘Umar (may Allaah be pleased with him) that the Prophet SAWS (peace and blessings of Allaah be upon him) said: ““Each of you is a shepherd and each of you is responsible for his flock. … A man is the shepherd of his household and is responsible for his flock.” Narrated by al-Bukhaari (2554) and Muslim (1829).
But some fathers fall short in that due to lack of awareness and poor judgement, or because they place excessive trust in their brother, or they feel that their brother has repented and regrets it, and that his molestation was just a mistake.
Do not hasten to accuse your father and think that he is neglecting his honour and that of his daughters. Try to resolve this issue by talking to him frankly and discussing with him, and seek the help of your mother and siblings. Try to convince him of the seriousness of the matter and that he should not take it lightly, especially since he did react, but his reaction was weak as you described in your question. Whatever the case, it indicates that your father is concerned to some extent.
If he wants to give his brother a second chance, that should not be by giving him permission to stay overnight at your house, for that is helping the shaytaan to gain power over him. Rather he should stay away from you and not mixing with you. If he wants to stay in touch with him, that should be between them, without you, the family members, having anything to do with it.
If your father insists – Allaah forbid – on bringing his brother to mix with you and welcoming him to your house, it is not permissible for you to keep quiet and agree in that case. You have to be strong and courageous so that you can complain about your father to the closest people to your family who you think are religiously committed, of good character and wise, and seek their help to resolve the problem that you are facing. You will certainly find someone who will understand the seriousness of the situation and will be the best help to you in sha Allaah.
Throughout all this you have to observe full shar’i hijab. In many cases molestation among relatives happens because of carelessness in covering the ‘awrah in front of them, so you will see a girl wearing very tight clothes, and uncovering her legs and arms and more than that, on the basis that she is sitting with her mahrams, but she does not know that the shaytaan may whisper to a person to commit every haraam action, and that a person may be tempted by what he sees of his mahram’s charms, especially if he is young.
You have to keep away from the places where this uncle of yours can see you, and cut off all ties with him completely. Do not sit in a gathering where he is, and do not say salaams to him. If you can find a house of one of your mahrams who is of good character and religious commitment, then go and stay there until this bad uncle leaves your house.
Here we should point out an important matter, if no appropriate action was taken to deal with this problem and if your father is negligent towards the misbehaviour of his treacherous brother; in that case we should point out that the responsibility for yourself and your religious commitment falls on your shoulders, and you should try to make up for this lack of protective jealousy on your father’s part and his failure to take good care of you and look after you, especially with regard to matters of religion and virtue, by maintaining your hijab, and keeping away from haraam mixing and being alone with a member of the opposite sex.
Allaah knows your situation, and He knows that you love modesty and hate immorality, and that you are striving to ward off all fitnah. He will decree your reward for that abundantly and in full, in sha Allaah, with no shortfall.
Allaah says (interpretation of the meaning):
“Verily, the Muslims (those who submit to Allaah in Islam) men and women, the believers men and women (who believe in Islamic Monotheism), the men and the women who are obedient (to Allaah), the men and women who are truthful (in their speech and deeds), the men and the women who are patient (in performing all the duties which Allaah has ordered and in abstaining from all that Allaah has forbidden), the men and the women who are humble (before their Lord ___ Allaah), the men and the women who give Sadaqaat (i.e. Zakaah and alms), the men and the women who observe Sawm (fast) (the obligatory fasting during the month of Ramadân, and the optional Nawafil fasting), the men and the women who guard their chastity (from illegal sexual acts) and the men and the women who remember Allaah much with their hearts and tongues.Allaah has prepared for them forgiveness and a great reward (i.e. Paradise)”
And Allaah knows best.