[akhtene]

Saruman settled in Isengard in 2726, after Rohan had suffered from invasions and Long Winter. Sone invaders,the Dunlendings came from Isengard. When they had been finally driven away by forces of Gondor, the Rohirrim were weakened and grieviously reduced.
Beren the Stuart was only happy to welcome a powerful friend at the border of the allied realm, which was rather helpless at the moment. The more so that Saruman was supposed to hold Isengard as Stewart's lieutenant.
I don't think that Saruman had to use any of his powers to convince the Stuart give him the key. At that time such an arrangement must have suited both (or better say all the three) sides involved.