Ask her if she has a plan for suicide, if she has the means to carry it out, if she intends to carry it out, and when. If her answers worry you even more, take her to an ER at once for an evaluation. Or you can call 1-800-273-TALK (National Suicide Lifeline) for immediate phone support.

Does she see a therapist? This would be a good idea in my opinion. I think it would be helpful for you to see one as well.

Also, I question telling her that her mother loves her, when she can see with her own eyes all sorts of reasons to doubt that this is the case. You discredit yourself in her eyes by stating what I would guess seems to be a evident falsehood to her.

I don't think you were necessarily wrong to explain about your relationship with her mother. I think that your daughter is old enough to understand what happened. But be that as it may, I think you should stop beating yourself up over that. You made a reasoned decision, the best decision you could make at the time. Move on from that, and don't help make it a permanent excuse or reason for your daughter to be unhappy.