Your actions whilst understandable, could be misguided so I would give this far more thought. Your reasons for this woman having contact are frankly poor and it could all too easily go so horribly wrong.
Your role as parents here is to protect your DD from such toxic damaging influences.
If this woman is too toxic for you as parents, then she is far too toxic for your vulnerable and defenceless child end of. You will not be able to clear the air because she is inherently emotionally dysfunctional to start with. Also she has not apologised to you both nor has taken any responsibility for her actions. Toxic people do not do this so the "normal" ways (which you are seemingly adopting here by expressing a wish to clear the air) of dealing with familial relations do not apply. These people do not and never do play by the "normal" rules governing familial relations.
This is from Lighthouse:-
A percentage of the general population is dysfunctional and/or abusive. That percentage, like everyone else, has children. Then those children grow and have children of their own. The not-so-loving grandparents expect to have a relationship with their grandchildren. The only problem is, they?re not good grandparents.
Many adult children of toxic parents feel torn between their parents? (and society?s) expectation that grandparents will have access to their grandkids, and their own unfortunate first hand knowledge that their parents are emotionally/physically/sexually abusive, or just plain too difficult to have any kind of healthy relationship with.
The children?s parents may allow the grandparents to begin a relationship with their children, hoping that things will be different this time, that their parents have really changed, and that their children will be emotionally and physically safer than they themselves were.
Unfortunately, this is rarely the case, because most abusive people have mental disorders of one kind or another, and many of these disorders are lifelong and not highly treatable. (Others are lifelong and treatable; however, many people never seek the necessary help.)
The well-intentioned parent ends up feeling mortified for having done more harm than good by hoping things would somehow be different ? instead of having a child who simply never knew their grandparents and who was never mistreated, they have an abused child who is now also being torn apart by the grief involved in having to sever a lifelong relationship with the unhealthy people they are very attached to.
More Here: lightshouse.org/lights-blog/toxic-bad-abusive-grandparents#ixzz2TFBKQrEX