I have seen the process of a resident being kicked out of an assisted living facility. The family of the resident was devastated.
For my situation, I know that the assisted living facility contract does in fact have several clauses in it that do specify in what situations a resident may be asked to leave ("terminate their residence"). Most of of the reasons for this have to do with disruptive behavior, dangerous behavior, or the resident not meeting residency requirements for the facility as defined by the state.
Based on what your mother wants to ask for I don't see that she would be kicked out. She's just asking to be an active part of the community and make friends, which most places welcome.
I very much agree with Ms. Lipani - you should advocate for your mother, assure her she perfectly fine to ask for what she wants, and encourage her to speak up for herself. (I know some of us have elderly mothers who have never done that for themselves so they now seem lost and uncertain about it at this stage of their life).
If you do in fact find the facility is not agreeable to improvements for your mother you absolutely should consider a different facility for your mother.
Best of luck to you and your mother, and take care of you as well as her.