Advice Needed - Problematic Coworker

I’m writing this post because I’m very confused as to what to do. Has a staff member who is a float who moves from room to room and this staff member is a problematic dishonest overall not a very good ECE. This staff member has caused issues with every single person in every room in the centre, causing issues and being nosy with others. With each issue she’s had with the other staff members. Our manager has conducted a meeting where nothing has happened. No reprimands were made by the manager and her behaviour has not changed. Unfortunately our manager is quite non-confrontational and doesn’t report or do write ups for educators who clearly break the rules. This staff falsely accused another staff of abusing a child and had the ministry of education come and investigate this certain staff member and also caused a serious occurrence where she lost a child and then proceeded to report it to the manager as if she was not the one to lose the child. This staff member has been in my room for a week and having her in the room causes quite a disturbance as she does not do her job as she lies about incidents and just overall does not supervise the children. So this past week I lost my temper at her because she left her shift 15 minutes early without communicating with any other staff member and compromising our ratios and she didn’t realise that the director of the of the company was in the centre so she ran back into the centre and pretended as if she was engaging with the children, so I called her out and she proceeded to lie to me and tell me that the time was something that it wasn’t so I pointed at the clock and asked her if she was blind. It was rude and unprofessional but I had been so fed up with her behaviour that I just lost my head. She then proceeds to go complain to our manager that I am rude and aggressive to her in the room and so we had a meeting with our manager where she obviously just denied everything and took no accountability for context. I am the youngest person who works at our centre so I understand working with older women they tend to overlook, my skills and speak down to me so I told her I demand respect otherwise I can’t work with her and I also reported to my manager all of the things that she was doing in the room and my manager did nothing. I’m planning on reporting this to HR on Monday, however I’m unsure because my manager hasn’t done anything and I don’t know how I feel about going over her head. I’m a very patient person however at this point I feel like her presence in the room is a disturbance for the children as she does things like give them her phone to play with during naptime does not change their diapers on time and other things I reported all of these things to my manager and she still has not done anything so I feel as though I have no option Other than going to HR reporting this and hopefully getting her fired. Am I doing too much? I don’t like dramatics and prefer to deal with things head on with respect and communication, but I feel as though this was the final straw to break the camels back.