The relationship was generally strained and complicated by the fact that Alexander II spent time grooming his eldest son Nicholas Alexsandrovich as the heir to his Great Reforms. Unlike Alexander III, Nicholas Alexsandrovich was reserved, witty, and had intellectual pretensions. This was a contrast to the very sullen and emotive Alexander III. His tutors, especially Pobedonostsev encouraged his Russophile tendencies and played on his Orthodox religiosity. The laws of succession meant that Alexander II had to bear his heir's increasingly conservative and Great Russian mentality. After his father's assassination, Alexander III preferred the company of gruff ministers like Sergei Witte (who never shed his frontier background) which was a stark contrast to his predecessor's cosmopolitan court.

As I answered a few weeks ago on the Great Reforms, the assassination of Alexander II and the conservatism of Alexander III have imparted a liberal gloss to Alexander II that he doesn't really merit. Alexander II turned increasingly against reform towards the end of his reign and the Great Reforms left many aspects of tsarist rule unchanged. In particular, despite all of the pretenses of the Great Reforms, autocracy was still sacrosanct in Alexander II's style of rule and non-Russian minorities (especially Polish and increasingly the Germans and always the Jews suffered from antisemitism) were still highly suspect within the empire . So a case can be made that the break between Alexander II and his son was more about style than substance.

Sources

Weeks, Theodore R. Across the Revolutionary Divide: Russia and the USSR, 1861-1945. Chichester, West Sussex: Wiley-Blackwell, 2011.

Wortman, Richard. Scenarios of Power: Myth and Ceremony in Russian Monarchy. Princeton, N.J.: Princeton University Press, 1995.