Your mother can receive a green card in about a year if out of the us. The "sister" cannot come with the mother. You could file for the child and the child would have to wait several years so they are unable to come together. I disagree with the other lawyer. I would disregard the other answer.
Your mother can get a green card. You can sponsor your sister too but it will take at least 10 years before she can come to the US
No, your sister cannot come with your mother, even if you file at the same time. Refer to the Visa Bulletin and you will see the that category (siblings) is very retrogressed and can sometimes take 10-15 years depending on the country.
Once your mother receives her green card, she can file a petition for your sister. This too can take some time (not as long as you applying for your sister) so I hope that there is someone in your homeland who can care for your sister.
You can file for your mother. It will take approximately 6-9 months. When your mother has her green card she can file for your sister. This will take some time but shorter than if you file for your sister. Speak with and retain an immigration attorney before proceeding.
212 537 4407
Legal disclaimer: The statement above is general in nature, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship.