How is it based on assumptions?
The OP says she heard her DD across the shop before she saw her, so the DD was therefore already tantruming and being very loud before the OP got anywhere near her.
The scene was already taking place because it's what the OP heard and what attracted her attention. It's why the OP went to investigate.
By the time the OP reached her DD, she says Jane's friend was dragging the DD by her hand. The OP says she saw this and I don't see any reason not to believe her.
The OP says she confronted Jane's friend, who is a stranger to both the OP and her ex.
And the OP says that within 30 seconds of this confrontation, Jane's friend was on the phone to Jane, who didn't answer the call.
And all three children then started asking to go home with the OP. So by her own estimation she was there for about 30 seconds before the children were asking to leave with her.
Jane's friend tried to prolong the scene by saying the OP couldn't take the children because she didn't know who the OP was, even though the children were all calling the OP 'Mum'.
OP took the children, as I suspect many parents in her situation would do, intending to call her ex from the car to explain.
I haven't assumed any of that, it's all in the OP's posts.
The children were either 'fine' as one poster suggested but still wanted to go with their mum. Or they were not 'fine' because they had just witnessed a massive scene, according to another poster, and still wanted to go home with their Mum.
But it's unfair to blame the OP for the scene, because she wasn't there when it started. She heard it after it had started and went to investigate. And asked some perfectly reasonable questions of Jane's friend when she got there.