Bankruptcy law requires that you list all assets & all debt. So of course, Mom will need to list both the house & the mortgage in her bankruptcy. I assume that she will continue to make the payments on the house so she can keep it, but the bankruptcy probably will show up on the mortgage.
If your step sister's name is on the mortgage, the bankruptcy will be noted on her credit report and may affect her credit. Since she did not file bankruptcy, she can dispute this & probably get the notation removed.
If your step sister is not on the mortgage, it should not affect her credit at all.
Mom needs to do what is best for her & stop worrying about what happens to your step sister!
Hope this perspective helps!
The short answer is yes, the house is an asset and must be included on the bankruptcy. If there is no mortgage on the on the property, it probably will not affect your step-sister's credit (since no bank is reporting on the mortgage). However, your mother may have to try to pull money of of the equity she has to pay her creditors. That is a question for her bankruptcy attorney and will be specific to her financial situation, the value of the house, and the bankruptcy exemptions to which she is entitled.
On a side note, I'm not sure how your step-father's half of the home went to your half-sister. If somebody dies without a will in Georgia, the spouse takes an equal share with the children, but never less than one third. So, assuming your step-father only had one child and that he and your mother each had an equal share in the house (one half), his half would have been divided between your mother and your step-sister, leaving your mom with 3/4 interest in the house and your step-sister with a 1/4 interest in the house. Were there other assets that were taken by your mother to offset the interest in the house? Also, your mother would have been entitled to a year's support from the estate prior to any split of assets.
I'd suggest setting up a consultation with a bankruptcy attorney to determine the best method of protecting the house. Many attorneys will do free initial consultations.
This answer is not intended to provide you with specific legal advice regarding your situation, or to create any attorney-client relationship.
Your mother should consult an experienced probate attorney to determine whether your half-sister actually even owns an interest in the house. It sounds as if she may have made an assumption which is not correct. As the second respondent pointed out, your half-sister would not normally have received your father's half interest in the house just because he died without a Will, although she might be entitled to a portion of it. Your mother could also have made a claim for a year's support, although if she did not do so earlier she probably can't now, since that claim has to be made within two years after her husband's death. She should also consult a bankruptcy attorney about the house, but it sounds as if there is some potential confusion going on here. Good luck to her.