My parents live in a two story duplex. The bedrooms are upstairs. My mom has dementia and it is getting worse. She burns things. Doesn't engage and my dad thinks he can make her remember. Neither should be using the stairs. But he refuses to do anything about it instead wants me to move home 18 hours away from my own grown children and take over so he can do as he always has sleep all day watch tv all night. No one wants to deal with him. He has been a stubborn selfish man my mothers entire life. I am the only daughter with brothers that none of us want to have to live with him but we love and worry about our beautiful mother that we know he is probably mean as hell to. Need a plan, advice, help.
Your father doesn't understand dementia: clearly he doesn't, if he thinks you can train somebody out of it. And "abuse is abuse, even if it is unintentional."
You don't need your father's permission to report concerns, and if APS agree that your mother is at risk of abuse or of neglect of her needs, they don't need your father's permission to intervene and assess her living situation. Tell them exactly what you've told us (apart from the stubborn selfish man that nobody wants to live with part! - the important thing is that he is neglecting your mother's failing mental health, and that both she and he are at risk if she leaves the stove on overnight).
My dad was the same - I put up with it till I caught her literally stuck on the stairs . I just told them both straight that mum wasn’t going up the stairs again. Moved her sheets, pillows night stand etc into a downstairs room made up the settee. Booked an appointment for an assessment and got a hospital bed in the room within 10 days.
No need to move - just be firm, ignore the crap, and get your mum a bed downstairs. If you can’t pop in each day to check she goes to her new bedroom then consider POA if not already done, and in the meantime share the cost with your brothers re evening care to assist her to bed.
When you say she burns things - is that food or because she smokes? I ordered in healthy microwave meals and put large labels on them just saying exactly what time to cook for their microwave.
When cooking if do more than you need - pack portions in plastic tubs with label of what it is and how long to reheat in microwave. As get into a routine can swap empty for filled tubs.
Its not ideal but a compromise
I get the idea that OP may fear for her mother’s safety and doesn’t trust her father’s care. Even though Mom may be upset by being relocated, people with dementia are relocated to facilities all the time and do well. Mom would be in the company of her children who obviously love her very much. She would be safe and well cared for.