Praise be to Allah.
We praise Allah, may He be exalted, for having guided you to Islam, and we ask Him to make you steadfast and help you, and to guide your parents and loved ones.
You should strive to call your parents to Islam and give them their rights of respect and kind treatment, as our great religion commands.
It is not permissible to sit at a table where alcohol is being drunk, because of the report narrated by Ahmad and at-Tirmidhi (2801) from Jaabir, according to which the Prophet (blessings and peace of Allah be upon him) said: “Whoever believes in Allah and the Last Day, let him not sit at a table where alcohol is being drunk.” In al-Fat-h, al-Haafiz Ibn Hajar attributed this hadith to an-Nasaa’i and classed its isnaad as jayyid. It was classed as saheeh by al-Albaani in Irwaa’ al-Ghaleel (7/6).
That is because drinking alcohol is a grave evil and a major sin; it is not permissible to do it or approve of it. The believer is required to denounce evil by taking action; if he is not able to do that, then by speaking out; and if he is not able to do that, then by disapproving of it in his heart, but in that case he must get up and move away from the place where the evil is being committed, if he is able to do so.
This is the general principle, that one should not sit at the table when wine is being drunk. So if your parents drink alcohol after the meal, then eat with them and leave before they start drinking. If they drink during the meal, if you can avoid sitting with them without fearing a greater evil as a result, then do that, and explain that your religion does not let you sit with them in that case.
If you are afraid that this may result in trouble and harm – and not just annoying them – such as them kicking you out of the house or being put off from listening to you when there are signs of their being interested in Islam, then it is permissible for you to sit with them, whilst hating it and disapproving of it in your heart.
You should explain the evils of alcohol and the harm that it causes, and the reasons why it is prohibited. Please see question no. 40882 for more information.
We ask Allah to guide and help us and you.
And Allah knows best.