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, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
There is no doubt that your father is in great danger for neglecting the prayer and consuming intoxicants. You are obliged to give him advice and remind him about Allaah and His severe punishment.
As regards going with him to Hajj, there is nothing wrong with accompanying him as it is not a condition that the Mahram with whom a woman travels be righteous; rather, she may travel with him even if he is Faasiq (a dissolute person) or a non-Muslim (but a non-Muslim should be prevented from entering Makkah).
Therefore, if you are able to go for Hajj and you have not yet performed your obligatory Hajj, you should hasten to perform it and not delay it until you get married because Hajj is an immediate obligation according to the correct opinion of the scholars of Fiqh. For more benefit on the immediate obligation of Hajj for someone who is able to perform it, please refer to Fatwa 87129.
Your father performing Hajj may be a cause for him becoming righteous and abandoning the sins that he is committing now. It is known from experience that many people who commit excessive sins become righteous after performing Hajj or ‘Umrah.
Sa‘eed ibn Jubayr interpreted the word 'upright' in the saying of Allaah (which means): {Allaah has made the Ka'bah, the Sacred House, upright for mankind…}[Quran 5:97] to mean, 'righteousness (for them) and strength to their religion'. So, we ask Allaah for guidance for us and you, and for success on the right path.
For more benefit on how to offer advice to one's father who is not abiding by the laws of his religion, please refer to Fatwa 21794.
Allaah Knows best.