Is it sufficient to communicate with one's sister despite inner resentment to avoid the exclusion of disputants from forgiveness on the night of mid-Sha'ban?

Your mother did well in her determination to end the estrangement. It suffices that she will not be held accountable for the hatred that enters her heart towards the one who wronged her, because it is something over which she has no control. Al-Qari and Ibn Hubairah clarified that enmity and love are not matters of choice, and that one who fears a person is not considered to be in contention, and similarly, one who wrongs another in a transaction does not reach a state of estr قطع (severance of ties) because of it.

Your mother should strive to remove the hatred from her heart towards her sister, unless it is hatred for the sake of Allah. And there is no sin upon her for what she finds in her soul towards her sister.