The woman is the type of person who falls for a guy but cannot express her feelings for him. It befits her character that she might sacrifice herself to protect the guy.
The woman did not know the guy, yet he showed up at her mother's funeral. Most likely he was around her age, or younger. If he was a friend of the family, or family, the woman would more likely recognize him.
Killing another family member is not something anyone does lightly. Perhaps the guy had a dark secret that was known only by the sister and she had to kill the sister to keep the secret from getting out. Maybe the guy murdered her mother (in front of the sister) or maybe she discovered the guy was a public figure and married and the sister was having an affair with the guy. In both cases, the woman protects the guy by murdering her sister. Unless she was protecting the guy, why else would she murder her own sister. Unless in a more extreme circumstance, like she found her sister trying to kill the guy and tried to stop the sister, killing her in the process.
"Own mother" could mean the sister had a different mother, but that her sister was unrelated to her or adopted, or that she was adopted, wouldn't be enough of a reason to kill her sister.