I'm not sure what you mean by "poking" the chick.
Was she aggressively pecking it? Mothers will remind babes to stay under them to dry off. As long as that is very gentle, all is well.
However, some hens remain in hatching mode and will strike anything that attacks their hatching eggs...including a newly hatched chick...if their wires get crossed....especially if there is another hen nearby. That kind of aggression is NOT okay.
So without actually witnessing the incident, my instinct tells me this particular mother may not be happy brooding chicks. Some are good incubators but poor mothers. The only way to know is let her have a chick and see how she handles it while carefully keeping watch.
Good luck with your new brood.
LofMc