Wanting:
100% agree with you.
I met, dated, got engaged then married in the space of 9 weeks, and it was good for the most part. The last 5 were hard yards and when retirement struck, he retired me for the wine. His love for it was stronger than for me, and by then my love and respect was down to near empty.
How do you "know" someone in a few weeks? You don't...not really...and you found that out when you discovered a couple of little things in her baggage....she had alcohol issues, she had morality issues and she is a good manipulator.
I think your ex should be congratulated for her determination to shield your daughter from any possible hurt, and I do not mean deliberate harm from your new gf. I meant of learning to like her, then maybe see her go off the rails and perhaps disappear out of view.
When you can honestly say you are sure of this woman's regard for you, she has shown her dedication to recovery....then look at your child's involvement.
And yes, I see co-dependent in the rose coloured glasses, and know what they look like as I have worn them myself. Later on you find the roses have bugs on them, and it depends on what bugs as to whether you still want the rose or not.
Take it steady, take your time and take your own inventory before you introduce your daughter into your fairy story romance.
God bless