My brother currently has dad in Indianapolis Dad called me indicating my brother was,"putting him out". Brother comfired I could have him and later he changed his mine. And wouldn't let me take my dad. I live in Las Vegas, Nevada, retired,and phyically and financially,capable of caring for my dad. My brother and wife works and my 92 year old dad is left alone during the datime.
In your title you wrote "POA/Guardianship". POA and guardianship are 2 very different things. In your situation, if you think your dad would be safer with you, you would have to apply for guardianship through the court system. You'd have to have a lawyer. This is a lengthy and expensive process. But from what you wrote this might have to be the way you need to go if you want to compel your brother to relinquish your dad to your care.
And then there's the question pamstegma wrote: what does your dad want? I understand that his Alzheimer's may inhibit his decision-making process but has anyone given your dad a choice? Live with son or live with daughter? Is your dad able to make that choice?
If that is the case, and if Dad is still of somewhat clear mind to understand what is a Power of Attorney, it is time for your Dad to assign someone to represent him in case there are any medical or financial decision to make when Dad is unable to make those decisions. Both you and your brother can have joint Power of Attorney if you and brother are usually on the same page regarding Dad.
You mentioned verbal abuse.... who is verbal abusing whom? If it your Dad that has become difficult to deal with that is very common with one who has memory issues. Or is your brother and his wife become burnt out taking care of his Dad? Again, very common.
No one is ever physically or financial ready to take care of an elder.
What I am saying is that he just might be at the place where the care at home by one or two people 24/7 may not be enough. I don't know, but a doctor would know. Have him see a doctor who specializes in gerontology, the medical needs of older people. .