I have been taking care of my mother with vascular dementia for 4 years. The toll on me and my life has brought me to the edge. My sister has been very critical of me and we have not spoken for years. Now that I am struggling so, she suddenly wants to 'talk' and take charge. I feel resentful and angry at her arrogance and judgement.
Who has POA for finances and medical? Are you privy to the will?
I see no harm in talking to see where she is coming from and what she offers to bring to the table. If you don't like it, offer her some alternatives, such as "gee Sis, I could use some respite time, glad you offered. What weeks or months can you care for mom?" or "Gee Sis, thanks for your offer, I think its time to get outside assistance with mom, I'm looking at 30 hrs, 40 hrs per week - its $20/hr -- how much can you kick in?"
My husband meanwhile has single-handedly taken care of her (in her home) on what came to be a daily basis (3x/day weekdays and almost all day weekends) while simultaneously holding down a full-time job, with virtually no support or respite for the past six years. The only time his sisters ever called him was when their mother had intermittent hearing trouble and failed to answer her phone. He eventually stopped calling them, because it usually wound up being a one-sided conversation. I'm not sure what they have against him, unless it's because (as the youngest and only boy in the family) his parents treated him more favorably (not saying that was the case; it may have just been their perception of things). Incidentally they all married and left the home early while still in their late teens -- not sure what was the catalyst for that.
But anyway now that Mom has been admitted to long-term care, we've received reports (from another residents' family, who were present at the time) of unauthorized visitors referring to her as "Grandma". :( It really concerned us, because the facility had no records of any visitors other than ourselves; and for all anyone knows it could've been some strangers posing as relatives for some ill-intentioned purpose. The facility where she is staying currently is almost a three-hours' drive from her home, and we don't know how they would've even found her unless her previous (transferring) facility had given out the information (which I'm not certain they were authorized to do).
Like Whitney suggested, I'm thinking that their reasons for showing interest now might not be from the best of motives -- particularly since they're still avoiding my husband (and after he had made special efforts to try and keep them informed during the first few weeks of when she'd gone through the crisis).
But relating to your own situation, in what way has your sister been wanting to "take charge"? Is it mostly the legal/financial stuff; or is it to share the actual caregiving load? If the former, I'd be very cautious before surrendering any control of your mother's finances or healthcare decisions over to her. If the latter, I'd still be cautious; but try to remain open to the possibility that she might just genuinely want to repair and re-establish her neglected relationships.