Older brother indeed should avoid any contact with radicals. But Nicholas II hardly would accept someone liberal-reformist as tutor of his heir. If then you don't make him more liberal or at least open-mind.
Perhaps Alexander II is not assassinated and he manage make couple reforms more. Alexander III reign would be pretty short if he even ascends to power. At least him is not going destroy all reforms what Alexander II did altough things would be stagnatised.
Few considerations:
1. There is no reason to assume that, absent the general background and his brother’s example, Vladimir would necessarily grow as more than an average liberal.
2. There is absolutely no reason to assume that he would chose an academic career and even less so that he would excel in any area making him a suitable candidate as tsarevich’s tutor: standard curriculum involved languages, religion, history, geography, some military education (mostly paradeground drill) and, as I understand, some rudimentary knowledge of the legal system and economy (not too much of it, judging by Alexander II).
3. Continued reign of Alexander II was a luxury that Russia could ill afford because thanks to his (and his brother Constantine’s) views and actions the country was facing both economic and political ruin. Russian industries were not developing being killed by the low tariffs on imports (seemingly progressive idea applied without bothering to think) and the budget deficit was steadily growing. Agriculture was in a bad state for many years after the Reform because, even with the available subsidies, most of the peasants still had been using the obsolete methods. The military reforms were right thing to do but the war of 1877 - 78 demonstrated a lot of flaws in what had been done. Constantine was, of course, a progressive figure but as an Admiral-General he wasted huge amounts of money building, as someone put it, “collection of the ships but not a navy” (to be fair, his successor was even worse). Russian foreign policy led to the international humiliation. Russian “society” (educated classes) was in a complete turmoil not being able to digest the existing reforms but demanding more and seeing its main purpose in life in opposing the government as a matter of principle. Not only would the juries let free not quite successful political assassins but after assassination of Alexander II there were voices for pardoning the assassins as a way to gain “public trust”.
4. There is no reason to assume that a railroad catastrophe which triggered Alexander III health problems was inevitable.
5. “Stagnation” is hardly a good way to describe the reign of Alexander III. He introduced quite a few reforms which triggered development of the Russian industry, turned the money-consumed railroads into the profitable enterprises, started cutting the deficit and, the 1st time in the modern Russian history provided soldiers with the simple and convenient uniforms (which survived through the revolution and all the way to the fall of the SU). He managed to put expenses of the Grand Dukes under at least some control and cut their number. He managed to restore to a great degree law and order and, unlike his predecessor and successor, managed to keep Russia out of wars while maintaining its high international prestige. Well, of course, there were no “reforms for the sake of the reforms” but, let’s face it, contemporary Russia needed slow changes even if the educated classes wanted “everything” (which none of them could clearly define) just now without thinking about the possible impact of these “social jumps”.