Will my fasting be accepted, and will my continued boycott of my parents be considered disobedience to them, taking into account the difficulty of enduring the situation and living with them?

The shortcomings of parents in obeying Allah or in fulfilling their child's rights do not negate their right to dutifulness and kindness. It is not permissible to abandon them or to be undutiful towards them. They must be advised with wisdom and gentleness, and efforts should be made to prevent them from committing sins, as this is part of being dutiful to them. The mother must be informed of the seriousness of sins and betrayal, and the father should be advised that his approval of wrongdoing within his family is a grave sin and distances him from Allah's mercy, for a dayyuth (one who condones immorality in his household) will not enter Paradise. You must repent to Allah for abandoning your parents and severing ties with them. Your fasting is valid, but its reward is a matter of scholarly disagreement, and likewise for prayer, as it is said that for one who sleeps while his parents are displeased with him, his prayer does not ascend beyond his ears.