Boney
I haven't made an assumption, it's all in the OP's posts, including the part about Jane's friend wanting to remove OP's DD because she was embarrassed.
The OP's child was loud enough to be heard and identified from the other side of a large department store. The OP has said that.
That would have drawn attention from more people than the OP, especially as Jane's friend and the OP's children had come down three floors in the shop during the tantrum (again, said by the OP, so not my assumption).
Scene wasn't my word to describe the situation, but we can call it anything really, a disturbance, a commotion, a tantrum, a woman dragging a strangers very vocal child along by her arm, whatever, but it was happening before the OP got there.
It's possible but unlikely that a group of four people, one of them screaming and being dragged by another, got through three floors of a department store without attracting any attention other than the OP's.
And she says Jane's friend was embarrassed by the tantrum, which indicates that yes, people were looking, people had noticed. So I haven't assumed that either, the scene was taking place and Jane's friend was embarrassed by it before the OP overheard and went over.
But lets say nobody else was paying them attention, either before the OP got there or afterwards.
Her elder two children had just witnessed their sister having an epic tantrum and be dragged along by a woman they don't know, having only met her once previously.
I can see why in that situation they might want to go straight home with their Mum when she appeared unexpectedly in the middle of all that and that's why I said that they may or may not have been fine but they still understandably wanted to go home with their Mum.