What legal steps do I have to take to make sure my sister is there to take Mom to her condo?

Pursue Guardianship. That way it is your call to move mom to Assisted Living.
Forget your sister, forget trying to nag her awake. Get the Judge to support the move to AL. My guess is she won't even show up at the Show Cause hearing.

Is your mother's so bad that she has been declared incompetent and thus not legally able to change the POA from your sister to you since you are the one doing the caregiving?

You cannot "make" your sister take care of your mother or have her move mom to AL. In my opinion personal wealth does not make one adult child more or less responsible than the other, but it is unfortunate the family is not pitching in equitably.

You cannot just play hot potato with mom either - you cannot decide sis needs to take her in.

All you can do is draw your own boundaries. You can advise sis that she has 10 days to make arrangements or you will.

Perhaps you can take a week vacation from work and dedicate it to settling mom in an AL. Does mom have the funds, or is the issue that sis was supposed to fund the AL? If mom has the funds -just do it, sacrifice a week and you will get a lot more time back, else you will be stuck.

I have been up all night at least 3 nights a week and the other 4 at least 3 times. I do the grocery shopping, laundry and go straight home from work every day so that the day care takers can go. On my days of whiich are 2 I sometimes take her to an assisted day care for 5 hours so I can clean, do the laundry change her sheets and go to the grocery store, so I think I get about 3 hours for myself. I am suppose to receive about $600 per month to go towards the extra utilities, food (for mom and the care givers during the day) storage rental for her furniture from when she moved in with me and half the rent of $390 . Last month I received $200. My sister is supposed to be setting up an assisted living place in Calif. so I was told 3 months ago but have not heard a word since. I am stuck and have no light at the end of this tunnel. I have to work full time to cover my own expenses What can I do so that my sister can take some responsibily for a while. She lives alone and has 2 bedrooms and 2 baths. In a beautiful secured building.