Spiridovitch records that at Livadia, Alexei could at times be very stubborn and could be demanding of those around him. He cites for example the time he ordered a soldier on guard duty on the Livadia grounds to march into the lake, fully clothed, up to his neck holding his rifle over his head. The solidier had nothing to do but obey him, however when Nicholas found out, he was furious and Alexei was severely punished and told that he must never order his soldiers to do anything like that.
Another time, Spirdovitch recounts how Alexei climbed up a tree (a major no-no given his hemophilia, lest he fall). He steadfastly refused to come down, and disobeyed all the servants who were trying to coax him down. Finally, the only way they got him out of the tree was by telling him that since he wouldn't come down for any of the staff, the staff would have to get the Tsar to come get him down, and Alexei would have to answer to his father. THAT worked and he came straight down the tree, rather than have to face his father for being stubborn to the servants.
A third time, in Yalta, Alexei won a bottle of champagne at a raffle at the White Flower Festival. He carried it around proudly, and kept wanting to open it and drink it. Alexei and Nagorny spent the entire day quarelling with each other because he wanted to drink his champagne and Nagorny wouldn't let him.
That said, Spirid. also recounts numerous times Alexei was very kind, gentle and charitable to the servants around him. Alexei was very proud that he was finally old enough to partake in the Tsar's daily ritual of tasting the dinner of the soldiers on duty at the palace. A plate of the same food the men ate was brought to Nicholas and to Alexei daily, so that the men on duty would know that their dinner was good enough for the Tsar himself. Alexei learned that the soldier who brought the plate to him daily had a daughter the same age as Alexei, and Alexei used to give him presents all the time for the man to give his daughter from Alexei. Sometimes, Alexei would go into his sisters' rooms and take THEIR dolls to give to the soldier's daughter!