Verified answer

The tough part will be convincing visa/immigration officials that your mother and sister will return to their own country. They should buy round-trip plane tickets. They also need to prove circumstances compel them to return home at the end of their vacation: jobs to return to (letters from their employers stating the dates of their scheduled vacations and that they still have jobs to return to), own a home, have a husband/father & younger children that need mom & sis back home, anything else that proves they are only on a brief vacation and will indeed return home.

Thousands try to sneak in the "back door" -- visit a relative and never leave. It is tougher to prove they will leave when they have a relative already in the US, than if they are taking the kiddies to Disney World for a week.

You will act as their sponsor for the duration of their stay. For procuring the visa, you will have to send them your signed sponsorship documents, a bank statement of the last 6 months (with a sizable bank balance) and they will also have to carry a Medical Insurance Policy for the duration of their stay in the US.

Presuming your mom and sis are from India, they will have to book an appointment ( usually weeks in advance ) and be at the Consulate, fresh and early, for their interview. Yes, an interview is conducted and the outcome is based solely on the discretion of the Visa Issuing Officer.