Alexei Petrovich, heir to Tsar Peter the Great, was essentially everything his father wasn't. Lazy, bookish, disinclined to anything military and raised by his mother and reactionary boyars to be against everything his father liked. However, what if instead of growing up hating/fearing his father, Alexei instead tried to be like Peter? The idea being that if he was into the same things his father was, then said father would want to spend time with him.
Remember that Alexei was OTL tortured to death for supposedly (or even likely) being involved in a plot to overthrow Peter and undo everything he'd done to modernize Russia. How does Peter the Great having a loyal heir dedicated to his style of rule affect the course of Russian history?