My mom recently moved from home to live with my sister in California. My sister attributes it to my mom wanting to get away from her ex. My mom says she wants to start a new life.

My mom has been living there for about 2 months and everything is going fine. It all started when they moved to Texas to be closer to my sister's husband's family and my brother. 

My sister is pissed because she claims all my mom does is stay in the room all day and texts her ex. She is mad because my mom doesnt even want to play with her daughter and would rather talk to her ex. The same ex my mom is on and off with over the years and would complain about her to us, her kids every so often. 

My mom says that she doesnt want to stay with my sister because she is too controlling and talks too much it is stressing her out. (I agree that my sister could get a bit too much at times)My mom says she wants to start working but requires a physical address. My sister found a place with her friend for 300 a month, my sister's friend just asks that my mom not stay some weekends so she could have alone time with her son. My sister offered for my mom to stay the weekends. My mom doesnt want it and to find a different place because she doesnt want to stay with her daughter and just live on her own. Note, my siblings and i will be paying for the place until my mom gets a job and could pay for herself and we are not exactly rolling in money. My sister's husband recently got let go from his job and they've been living off their savings. 

My sister and mom got into a screaming match this morning because my mom didnt want to go to her in-laws wedding and would rather look for a job. My mom is currently in a hotel for the night.

Am i the asshole for thinking my sister is in the right?