Power of Attorney questions and sibling issues...

Hello,

My 86 year old mother has advanced dementia and lives with me. I am the middle child with a younger brother and older sister. 

My brother and I have jobs and younger children to take care of and he also comes over to help with my mother. Our older sister is quite a bit older than us, has grown children and is retired but does little to assist with our mother.

Last year our sister, Darlene, took our mother to the bank to add herself to her banking account. The statements now go to her house (this is the acct where her SS checks are directly deposited) and she's the only one with online access to our mother's account...even though she lives with ME! Now Darlene has been telling other family members (has not said a word of this to me or my brother) that it's time for her to get Power of Attorney over my mother and "it has to be her because she is the oldest." I have seen in the state of CA that it can be shared between siblings which obviously my brother and I would prefer but here are my questions:
1. since she is already discussing this with aunts & cousins rather than her siblings, can she do this behind our backs?
2. Would me and my brother have to agree to it before she could obtain power of attorney?

As you can probably tell, we are not comfortable with her "being in charge" and the fact that she is discussing the matter with everyone but is makes us believe she is up to no good.

Thanks in advance for any insight.

Jenny Ann