your father likely drinks to excess because of trauma in his life that few other than him are familiar with, he lies about his relationship with you because when he is not drunk and thinking clearly that is probably the relationship he wished he was able to have, now that he is in his 70s his life consists of sitting around remembering all of his regrets.
i don't know the extent of your relationship or estrangement, however your mother is right if you do not reconnect with him after he dies you will wish you had, and when you are in your 70s that will be one of the things you wished you had done differently. even if he was a mega prick your whole life, take the high road and be there for him when he needs you to be. a balanced and confident man does not let their father die alone if given a choice, show him you are that individual whether he admits or not your presence will be appreciated by him and he will be proud of you.
take your ass to the hospital with a bottle of his favorite hooch and get ***** with your dad, seriously.