My sibling states that she has a POA over parent but will not let any other siblings see it. She also will text us to say that my parent is a lunatic and bat-sh-t crazy. That concerns me because not parent is not a lunatic or crazy. My parent has dementia. I think it's horrible for the sibling who has POA can make statements like that about our parent to us This is very concerning to the rest of the family. This sibling should have a bit of sympathy.
Does your sibling live with your parent? If so, she could be burning out from the amount of care your parent needs. Dementia means that your parent may say do awful things all day long, with no remorse, since the disease robs them of their ability to empathize with others. It takes away their inhibitions, reason and logic. Which leaves a hot mess that drains the life out of their caregivers if they don't have enough support and breaks. Maybe ask your sibling if she needs help?
You should tell your sibling that once s/he lets you see the POA document, that you will happily & gladly take over ALL the care and management for your demented parent on a 24/7 basis. That should do the trick in getting your sibling to send you a copy of the POA document in short order.
This sibling should have sympathy, but she deserves sympathy from the rest of the family, too, since it sounds like she's doing all the work. It's incredibly hard to deal with dementia. She might be venting. She might be abusing your parent. It sounds like you don't have enough information or involvement to know what's really going on.