Even if she did she was not in a position to carry out any such threats. I she had said "I have a bomb" or some other such serious threat it would have been made public by the police. I think that you are grasping at straws. It does appear that she did deserve to be arrested. Another article on the topic:
2 workers on leave over video showing boy wrenched from mom's arms
"The Brooklyn Public Defender's Office says the mother, Jazmine Headley, had taken a day off work to go to the center. She was trying to determine why the child day care benefit she had received for her 1-year-old son had been cut off.
The defender's office says Headley, 23, was sitting on the floor because there weren't enough chairs in the busy center. She was asked to move multiple times as the situation escalated, and eventually security called 911."
I do not remember if I posted a link, but she had been arrested earlier for a credit identity theft. If she was working a scam it seems dubious to me that she was employed. Perhaps she lost her benefits since she was not working and did not need them. At any rate she was far from innocent, but the police still had to treat her like any other human being. They had more than enough to gently force her out of that office once she was arrested. No need to use force on the child.