Vlad and Radu were left with the sultan by their father as a kind of collateral. Vlad Sr. was technically a vassal of the sultan, but he had a tendency not to do what he was told, so the hostage thing was his way of saying he was going to play along from now on. As hostage situations go it was quite cushy: Vlad and Radu got first-rate educations from the same tutors employed to teach the sons of the Turkish elite, including the sultan's son, Mehmed II. That Mehmed liked Radu is not surprising because everyone liked Radu, and not just because he wasn't Vlad, though that was probably a bonus: Radu had been called "the Handsome" since early childhood, and was apparently charismatic in addition to being a looker.
In my version of the story, as you can see, Radu is perfectly happy with his situation, though of course that's not necessarily how it really happened. After all, Mehmed was the sultan's son, and the sultan pretty much owned Radu, so who knows how coercive things got between them? Even such an evil act would have been a drop in the bucket in the wacky burying-people-alive nailing-hats-to-heads world of fifteenth-century Turco-European politics. (If the Turks really didn't like you, they sawed you in half.) The authors of the Dracula biography I'm reading seem to think Radu became Mehmed's lover as a means of gaining political capital, which is another plausible interpretation. Hell, it could have been all three: Radu could have liked being Mehmed's boyfriend, and been afraid of the consequences of refusing him, and hoped to gain lasting favor from the relationship that would enable to him to succeed his father as ruler of Wallachia. People are complicated.
Wallachian succession, by the way, was endlessly complicated by one simple rule, much as National League baseball is made far more complex (and interesting) simply by the fact that pitchers have to bat for themselves. The rule was that any son of the current ruler could succeed him if the boyars, the oligarchs, decided to elect him. Even bastard sons were eligible. So not only were potential heirs constantly watching their backs because it might turn out that the scullery maid's son could cut right to the front of the line, but it was in your best interest to kill as many of your brothers as possible -- as many as you could find, anyway, because there are a lot of scullery maids, and rulers get around. Also the boyars usually wanted to elect the weakest candidate they could so they could pull his strings, so the game was to act pliable before they picked you and then impale the shit out of people afterward so everyone was too scared to oppose you. Insert joke about contemporary politics here.