Is the quarrel and estrangement that occurred between me and my neighbor, after her repeated mistreatment and my request to cut off the relationship, considered unlawful desertion that prevents forgiveness during blessed days?

If a woman harms you with insults and backbiting, then there is no sin upon you for shunning her, and this will not prevent forgiveness, Allah willing. It is sufficient to greet her upon seeing her to remove the label of shunning, according to many scholars. And you should abandon obsessive thoughts if that repels harm.