In canon, Jacob’s reason for sparing Renesmee (or Elizabeth, as I renamed her in a previous post and as I will refer to her from here onward) is because he imprinted on her. For those who don’t know, imprinting is what happens when a shapeshifter encounters a certain individual. That individual becomes the center of that shapeshifter’s universe, to the point where he (or she, in the case of Leah Clearwater) will do and be anything for that individual, ensuring that he/she is happy, healthy, and safe. A lot of people cry pedophilia when thinking about this devotion that Jacob has towards Elizabeth, which Jacob himself states is not the case at all. My solution is to remove the imprinting instinct from this situation and have Jacob’s love for Bella be the thing that stops him from murdering her child out of revenge for her supposed death. Of course, Jacob’s love for Bella will still linger until he imprints on someone else (preferably another adult, like Lizzie, the girl he met earlier) or just finds a way to move on and pursue a relationship with someone else, never finding his imprint.