All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger.
There is nothing wrong for a woman to seek the help of another Muslim woman to remove her hair from parts of her body that are not considered 'Awrah (parts of the body that must be covered), otherwise it is forbidden for her to do that in the parts of her body that are 'Awrah.
The woman’s ‘Awrah in front of another Muslim woman is the area between the navel and the knee, according to the majority of scholars.
However, some said that all her body is considered 'Awrah except of what she is allowed to unveil in front of her Mahrams (permanently non-marriageable men). This refers to the parts of the body which woman normally expose in their houses when doing their chores. This is the view adopted by the Permanent Committee as well, which issued a Fatwa in this regard.
So, based on the first view, it is not prohibited for a woman to remove her armpit hair with the help of another woman. However, based on the second view, such an act is prohibited because the armpit is considered 'Awrah.
There is no doubt that the latter view is better. It protects and preserves a woman's bashfulness, and it is best if she wants be on the safe side. Therefore, a woman should not uncover her armpit in the presence of another woman in order to remove its hair, because she can remove it by herself as it is something easy and does not require much effort.
Allah Knows best.