How should a questioner's relationship with his mother be, and is it obligatory to visit her, knowing that she is ill-tempered, caused her divorce from his father, and does not care for her children?

Allah Almighty commanded to accompany parents with kindness in this world, even if they strive to make their child associate partners with Allah, but He forbade obeying them in disobedience to Allah. Therefore, the disbelief or فسق (transgression/immorality) of a parent does not negate the duty of righteousness and kindness towards them. The questioner is advised to maintain ties with his mother and be kind to her, and to employ the best methods in advising her, hoping that Allah may guide her through him. He should not neglect this, fearing regret if death overtakes her while she is in that state.