Who retains custody during a custody case?

First of all, I want to say that at this time, I am caring for my daughter. My daughter has been solely with me for about a month now. Mom has had a few visits but has been absent for the majority of the month. Mom has mental health issues and was hospitalized. Mom planned on coming back home with us but I felt it best that she didn’t. Her mental health is not stable and I feel it is detrimental to my child. Child protective did get involved because of Mom. They did an assessment and determined that Mom should not be alone with daughter for the sake of child’s safety. Child protective also said visits with Mom need to be supervised. They dropped the case and sent me a letter stating the former.

I broke it off with Mom because the relationship has been over for a long time. It wasn’t good for any of us and we all needed change. Mom is staying at her mother’s house.

Now, to my original question. If I go to the court and petition for sole custody, will they grant me temporary custody until a decision is made? I don’t want Mom or Mom’s family to come and snatch my daughter. She should be with her father, not with her mother. Mom, like I said, has serious, debilitating, mental health issues that have progressively gotten worse since the death of her father a year ago. Mom has always had issues but never with this level of intensity