I agree about jenny, carol and John. One moment mercy killing is murder, the next, it's fine because Carol has admitted to, um, murder.
So, I think what it was really all about was jenny feeling her position as Queen Bee of a certain social milieu was being threatened by Carol. She felt Carol was going to usurp her in some ways just by being there and, felt threatened by Carol's knowledge of whatever happened between Jenny and John, long ago. That she might make it known, threatening Jenny's 'saintly wife' image and that Jenny wasn't sure how Carol felt about her as a consequence, perhaps resentful. Carol was too independent to be assimilated and controlled that way, so jenny sought to keep her a little outside nice society through rumour and exclusion.
What made all the difference was Carol taking Jenny into her confidence and saying 'look I know you think and having been saying this about me, that does bother me, so I'd like to set you straight'. Ergo, Carol showed that she minded about Jenny's opinion of her and, that she had nothing on Jenny that she was holding in reserve to smear her back with. Essentially Carol capitulated to jenny as queen bee, rolled over and let jenny rub her tummy. Social order is restored.