Okay, so the bottom line is: your sister is Bi-polar and does not get treatment for it, and this is something that hardly anyone, can handle. Regardless if she is your sister or not.
Regardless if you are living together or not. Even if you are not living together there will be relationship and boundary problems. Because she is mentally unstable...and is not getting professional medical treatment or therapy for it.
Hence, it will be a CONSTANT vicious cycle. Constantly.
Why? Because, your sister has a mental condition. And only a Professional can help her. She is not rational. And you and your Mom/sister are not "Professional" mental health experts either... thus, none of you can or will know how, to deal with her. No layperson, relative or not, are experts at dealing with this problem that your sister has.
Except that, you all are... feeding into it and everyone is toxic to each other, because, of your sister's condition. It is too much. It is too, much. For any layperson to digest or handle.
Even if you were the most perfect and pleasant person who had 100% perfect social skills and logic and lifestyle... this would still be, a very hard situation and a very hard thing to deal with.
Your sister herself does not know how to deal with it. You, your Mom, your other sister, don't know how to deal with it. And your poor child, is a spectator to all of this.... and she is a bystander to all of this dysfunctional behaviors. But you know this is not good for a child.
Even if you do move out and with your child, your sister will STILL be Bi-Polar. So, know that. But then, by being in separate living places than her, you can have your own environment to live in and with your daughter. DO NOT, live with your bi-polar sister.
The problems will NOT end.
Know that.
You live with your sister now. And it is awful.
And then you both are supposed to go live somewhere else and sign a lease together with your sister for another place.
Why?
Don't do it.
DO NOT LIVE WITH YOUR SISTER.
Even if she gets proper medication.
DO NOT, live with her.
If you do, you AND your daughter, will forever be tangled up in your sister's life and problems. Constantly.
Go find somewhere else to live. Not with your sister.
And do NOT feel guilty about it.
And do NOT let your sister hang a guilt trip about it around your neck.
Do not, get roped in to this.
And it is really an ugly situation to have your daughter grow up in.
Don't be a hostage to this.
*ETA: J., also know that, when some people are subjected to being around a mentally ill person all the time, then "you" can become mentally ill yourself in a situational manner... and then you too, begin to lose all sense of normalcy. And this is not right for you, nor for your daughter. Nor for her to grow up in this manner. It is a convoluted dysfunctional upside down toxic thing, for your daughter to be in and around, daily. Or forever.
Even expert mental health Professionals, cannot "fix" all people. And even they have a hard time, changing them.
Know that.
And it takes YEARS, for a professional to even help or improve a mentally ill person. And it takes CONSTANT treatment.
Don't subject your daughter to this, for years. It will not, end.
Your daughter, needs a NORMAL life.
Just get away from your sister.
Do NOT live with her, anymore.
Your Mom and sister can deal with it.
Don't be the one who has to do it.
You need a NORMAL life for your daughter.
Don't let them make you feel guilty about it.