Will the woman be held accountable if she expels her atheist sister-in-law from her house, when the latter might commit suicide or similar acts?

If the wife's sister is an atheist, she is in great danger. If her heart is devoid of faith, it is not surprising for her to commit suicide.

It is recommended to be patient with her and pray for her guidance, and to continue advising her gently, reminding her of Allah and warning her of His punishment.

It is best to assign someone skilled in debating with atheists to engage with her. If she persists in her error, she should be avoided and shunned. There is no sin in expelling her from the house if it belongs to the wife, or refusing her residence if it belongs to the husband.

If her expulsion leads her to commit suicide, then she is the one who transgressed against herself, and there is no sin upon the one who expelled her.