Assuming Alexander survives you still have a reactionary Cesarevitch who is moving further and further away from his father's policies - if for example Alexander II decides to create his second wife Princess Catherine Dolguriky, Princess Yurievsky, Empress then you would probably have an open breach between father and son.
Alexander III's eldest son Nicholas was educated and brought up to rever his father and grandfather but essentially his political education was grosly neglected and would probably be in either case.
With Alexander II living there is also a strong chance that his son with longer as Cesarevitch would not necessarily develop the severe ill health that lead to his premature death in OTL.
Also in 1881 Alexander II is actually 63, which in fact was quite elderly for a Romanov, so his lifespan is going to end within the next few years either way (his father was dead at 59), which still gives you the problem of dealing with a reactionary Czar in Alexander III at some point in the 1880's.
If you want a lasting political change in Russia in the late 19th Century you need Alexander II's eldest son Nicholas (II) to survive his illness in 1865 and proceed to marry Marie of Denmark (Empress Marie Feodorovna in OTL) or at a push have Nicholas II killed in Japan in 1891 meaning on the death of Alexander III you get Emperor Michael or have Nicholas die of typhoid in 1900 (although by then it might have been too late for change in Russia)