I guess my first question is would you and your sister be willing to sit down with your parents together and talk about planning for the future. Yes, it is their money, and yes, as long as they aren't incompetent to handle their affairs (and foolishly spending money would not be considered "incompetent" by the courts), they are free to do what they like.
What bothers me is the statement "she will be their nursing home if it is needed." That isn't even a realistic statement. Your parents cannot possibly predict the level of care they will need in the future. You already mentioned that your father's health is somewhat frail. I can share what happened with my folks (who kind of sound like yours). Like you, we grew up poor. My mom remarried when I was in my 20s to a man I call dad and all of a sudden, my mom was "upper middle class." My dad had over a million in retirement, but lost a large chunk when 09/11 happened, but was able to salvage over 1/2, plus rebuilt it until he retired. My dad worked until he was 70 1/2 and was a hale, healthy guy. When he retired, my mom was still working a great professional job, and my dad was getting several pension checks plus social security. My mom is 10 years younger than my dad, so working was still an option for her and she didn't want to quit, but wanted to work until she could collect her full SSI benefit as she doesn't have much in the way of retirement accounts. My dad had a stroke 6 months after he retired, then got stroke related dementia, and then also got Alzheimer's. Then he was diagnosed with severe COPD. Within a year after retirement, my mom couldn't leave him alone for one second. He ran away, crapped in the neighbors yard, tried to burn the house down, and finally when he attempted to strangle my mother, I forced her to put him in a nursing home. He is still alive 5 years later, and his bill? $10,000 a month for his care. The retirement? Nearly gone. My mother will be left with almost nothing and in a year my dad (if he is still alive - we are amazed daily that he is still with us) with have to move to a "waivered bed" because the money is all gone.
Don't assume that your sister can be their nursing home. It takes a team of people to care for my dad - unless your sister can provide that in her home and be willing to pay for it, I wouldn't count on her being able to care for your parents.
I would at least make the attempt to bring your folks down to reality - if nothing else, you and your sister shouldn't enable their poor spending habits.
Good luck!