Power of Attorney given to me by sister who is not competent some days.

You are correct that her best interests lie in being in care all of the time; it would be impossible to otherwise "guess at" her need to be in care. It may be, however, if her mentation fluctuates to this extent, very difficult, without letters of incompetency from two examining doctors, to get sister into placement against her will.

I would start with going with your Sis to visit places where she might stay. I did this with my brother when he made me POA when first diagnosed with "probable early Lewy's Dementia". He came over time to understand that without a support system, and with his very poor balance, he was no longer safe in his small home; he also knew, with me living other end of the state, he wasn't safe depending upon neighbors. He can to accept and choose the place he liked best. We were lucky it went so well. It is a place for you to start, and see how it works out.

First, you need to read your PoA document to see what authority it confers (like, does it allow you to do real estate transactions? Investments? or only pay bills and sign checks? The you need to see what activates the authority. Most common is 1 official diagnosis of sufficient cognitive impairment. See if it gives you both medical and financial. Now you need to know if she is able to afford AL. Eventually she will need MC, which costs more. LTC can be covered through Medicaid, if she qualifies, and hospice is covered by Medicare. Please know that being PoA does not mean you yourself needs to provide the in-home hands-on care for your sister (and this is probably why she is resisting outsiders, because she wants you). You can tell her that accepting outside aids is the only thing that will keep her in her house as long as possible. I tell this to my 96-yr old Mom when she resists solutions that I've worked hard to put into place. Then she acquiesces. But maybe your sister's impairment may be too far along to reason with her (or her short term memory doesn't allow it to stick). Then you do what's best for her without trying to get her to buy into it.