Although I have tried to talk around it, the following could be considered spoiler material.
All that about the daughter is true. Everything she told Carl sounds designed to pull his strings, especially the rape situation. And the way she kept trying to get Carl to leave could mean that she didn't want to be put in the position to betray him. But if Alpha wanted the girl to be trusted, she went about it the wrong way.
I suspect that everything is what it seems and that for all her talk, Alpha has doubts, especially after seeing Rick's society. I don't think she even believed what his people has accomplished was possible deep down, and is stewing in a deep pit of denial. I think that's why she did them all this way. Survival of the fittest means that if her way is wrong, it deserves to be taken down. So she made a move that was both a warning and an invitation to war, and left the decision up to Rick.