You need a lawyer ASAP. Forget about the DVC, that's not the big issue.
You need to also involve the Elder care authorities in the state your mother is currently being housed. . What they are doing is potentially illegal.
Failure to use your mother's assets to care for her is "theft"
Having your mother, who has dementia, sign ANYTHING is fraud. To sign something like that the person must be of "sound mind" She cannot sign a POA if the statement that "she has dementia" is correct. Moments of "clarity" do not mean the person understands legal documents. if your mother has dementila only a court can sigh the POA.
I would call the institution where she is staying and ask some POINTED questions. Question #1 WHO is paying the bills. if they have claimed she has no assets and have her on Medicaid you have even more issues! Ask them if they have the POA? Ask them if they have visiting hours. Without a court order I don't think they can deny you a visit.
Get a lawyer and protect your mother IMHO then worry about DVC!
Lawyer up is right and get a court appointed guardian for your mom.
I agree with all you've said about being careful as to who's on the membership. I really hope things work out for you and your mom. DVC is just a luxury that can be replaced. Your mom can't and neither can your other family members even if they are being a bit... err... bratty right now. 
I know that my mom's standard of living is not what she had or was expecting to have!
