OP, unfortunately the problem has arisen because of your poor boundaries.
This woman is pushy and sounds absolutely awful.
She is demanding your child at hers but refuses hers at yours?
Why wasn't that a huge red flag?
I think you need to clearly spell out your concerns about this woman to your daughter.
Her not accepting No and calling you was your time to push back hard.
This has gone on years and I came across a bit of it with a similar parent, but I just said no to her taking the girls to things.
I just said no thanks to the lifts, we will make our own way there.
She sounds deeply insecure and unfortunately by giving in to her for so long she has become emboldened over the years.
Speak honestly to your daughter about your concerns.
Have her watch the videos mentioned above.
Unfortunately it may be difficult for your daughter to see your point as you have allowed it to go on for so long.
I certainly would have felt deeply uncomfortable about someone who wouldn't allow their child at ours, but was so pushy about my child being at theirs.
I would have had enormous reservations and would have stopped it.
This woman doesn't care about you in the slightest, stop caring about her.