It is compulsory to abide to Islamic rule in every circumstance. Attending a party of close relatives which included sinful acts is not permissible.
Obeying Allah is above pleasing any one else.
You must keep on trying and trying to apologize from him and get his pardon. Allah (SWT) orders us to be nice to our parents even if they are non believers or wrong doers. You should not join their wrong but you must deal with them in the best way. Seek help of relatives and friends who can talk to him and do everything possible to make him forgive you. It is not an option but an obligation of the top priority.
You must (as a compulsory duty) keep in touch with all your relatives even if your parents do not like some of them. Cutting ties with any of your relatives is a major sin. Your parents are not allowed to cause or order any sinful act because the obedience of Allah (SWT) is more important than obeying your parents.
You should not do any thing which degrades your parents like criticizing or blaming them.
You can keep in touch with such relatives who are disliked by your parents, without announcing, to avoid hurting the feelings of your parents.
Yes, it counts as weak or poor relations with kin, which is very bad.
We must be always in contact with our relatives in usual way which are applied and accepted by our society e.g. visiting them, talking to them on phone, texting them, emailing them, writing to them etc.
It is good to treat him/her with respect and maintain some form of communication or offer assistance if it is necessary. However, silat al-rahm (maintaining family ties) is a rather broad concept which can be done in many ways. It is not necessary to have a close or frequent relationship. You can weigh what is appropriate for your situation. In some cases, the use of technology (such as e-mail) can help in being a safe and controlled way to manage the situation.
The primary thing that the Qur'an empahsises is respect and secondarily compassion. It is also related in hadith that if a person is dealing with parents who beat them, it is best to say "May Allah forgive you". That is, it is good to try to let go of resentment and move towards forgiveness in cases where the parents were not ideal.
For some people, one of the tasks of adulthood is to come to terms with the fact that parents are flawed human beings, like everyone else. We are usually more accepting of strangers with major flaws, but it can be difficult to accept this in a parent, because a child looks to a parent as a godlike figure and provider. The shifting power dynamic in adulthood can help with this, since once someone is no longer in need of their parent for their survival, it is easier to be more objective and accept things as they are.
Generally, as we progress through adulthood, it becomes easier to recognize and sidestep unhealthy psychological behavior (for instance, being pushed to enable an addiction, relive someone else's trauma, and so forth). Of course you should not participate in haraam activities; generally, as we get older, it gets easier to draw personal boundaries and assert that there are some things we will not do.
Whether we like it or not, our biological parents are our biological parents, we share some things with them, and there will always be a link. Cutting off ties does not change that. It may suppress the situation or make it no longer a practical concern and may result in more peace of mind, but the link and impact still persists psychologically.
Also, if you have children, it is healthy for them to have some contact with their grandparents. True, some people do keep children away from their grandparents if they feel they are a bad influence (you mention haraam activities), and this also has to be weighed; but keeping them fully in the dark about their ancestors leaves a blank spot in their minds and sense of self. It also increases the likelihood that the same pattern will be enacted by them (even if you are a good parent towards them). They will subconsciously copy your actions. Similarly, if you speak respectfully of your parents (even if you may feel anger), they will learn that attitude towards parents, but if you speak angrily and critically of them, they will learn that attitude towards parents.
Anyway, life is challenging, and the world is far from ideal. Perhaps the best way to handle the situation for now is simply to pray sincerely for guidance and to see where that takes you.
It depends upon the reason. It is obligatory for a Muslim to defend their honour. They are not allowed to accept being humiliated. Ayatollah Dastghayb Shirazi mentions situations where it is wajib or permissible to do qat' al-rahm: 'to cut off ties': that is: if you are forced to commit haram by your family and if your family drives you out due to your religion. If you are being seriously emotionally or physically harmed by a family member, then it is technically not permissible for you to tolerate that. Please see this link below for more information: https://www.al-islam.org/greater-sins-volume-1-ayatullah-sayyid-abdul-husayn-dastghaib-shirazi/seventh-greater-sin-qata-ar#what-least-amount-silet-ar-rahm-wajib
Cutting off contact with any of your relatives is a major sin which leads to very dangerous consequences :
1. To be cursed by Allah, according to Quran (Sura Muhammad, verses 22 and 23).
2. Your life span can be cut off, according to many authentic Hadeeths.
3. Your income will be cut off as well.
We should not cut ties with any relative even if they are bad to us and call us Kafir.
Our behavior should prove to them and other relatives our real identity and whether we are Kafirs or not.
Ahlul Bayt (AS) taught us to mix and treat our relatives and tribes with best manners. People wll then know the real teachings of Ahlul Bayt by seeing the good practice of the Shia.
If it is your house, then you must have authority over what enters it and what happens inside the house. Instead of getting to the stage of disowning, or expelling them from your house, try to get them to compromise.
For example, ask them to cook their non-halal means outside.
Also, continue to do as much dua for them as possible, that Allah ta'ala enlightens their heart and guides them. Remember that the dua of a parent is always answered.