Remember Mrs. Peters' comment that you refer to in your question title:
Mr. Henderson said coming out that wahat was needed for the case was a motive, something to show anger, or - sudden feeling.
It is highly significant that practically straight after she says these words they find the sewing. Note the irony too in what Mrs. Hale says, resentfully:
I don't know as there's anything so strange, our takin' up our time with little things while we're waiting for them to get the evidence.
It is then, precisely while the two woman are taking up their time with "little things" that they discover that the "little things" hold the key to the motive, as Mrs. Hale discovers:
Mrs. Peters, look at this one. Here, this is the one she was working on, and look at the sewing! All the rest of it has been so nice and even. And look at this! It's all over the place! Why, it looks as if she didn't know what she was about!
Note what happens then - they look at each other significantly and then Mrs. Hale begins to repair the crooked sewing. It appears, after all, they have found something to show sudden feeling or anger - the motive.