Is it better to have Mom stay in hospital or go home?

Recently, my mom fell and tore a large muscle in her hip. Because of the lack of mobility, she was admitted into the hospital. They discovered her oxygen is low so she is wearing oxygen now. Also, her confusion has gone up 100%. I have never seen her like this. She was slightly confused before she went but now it is off the wall. I have been able to find around the clock care for her at home. I became exhausted and needed the respite. Now that I feel better I am thinking it would be better if she were home. I do worry about her taking her oxygen off as she is doing at the hospital and more falls. I am really baffled and don't know what to do.