I think that Verin did not use Compulsion on Alanna for a few reasons. 1.) Right after Alanna bonded Rand the beginning of the next chapter was in Verins point of view. On pg. 210 Verin asks Alanna why she bonded Rand. "While you are thinking, answer me this. What were you at, bonding him like that?" Verin asked. If she had used Compulsion, she would not have had to ask any such question. 2.) On pg. 211 it says that Alanna had many weeks near Perrin but a life threat from Faile had stopped her from bonding him. It said that it had probably been over "frustration over that plus the frayed state of her nerves that led to what she did to Rand." So I think that this means that she didn't use the Cumpulsion. 3.) A final note. If Verin had used Compulsion it was probably to get a sort of tie on Rand, through Alanna. If Alanna had been Compulsed then Verin would have no need to ask all these questions. A question just arose in my head. If Verin used Compulsion to (as I think) get a tie on Rand. Then why didn't she just do it herself.