We don't know for certain WHY she was kicked out in the first place. If it had been simply for trying to stage a coup and kill Simba, I don't think she'd have sang "I've been exiled, persecuted, left alone with no defense. When I think of what that brute did, I get a little tense!"
I think she truly thought she was mistreated. Heck, this whole "avenge Scar" thing could really have been a cover for her trying to avenge her own personal slights. (I'm not so sure that Scar would want Zira so needlessly endangering the lives of his own children just to get at Simba.)
If it had just been Scar's death, why did she mention slights against her before even mentioning Scar by name "Scar is gone, but Zira's still around" was like in the second verse of That's My Lullaby.
And if Simba had indeed kicked Zira out merely for liking Scar, then Simba, in a way, created his own monster in Zira. Perhaps if he'd not done that, she wouldn't have wanted to off him.