Is not inviting a friend to a brother's wedding considered the beginning of severing ties with her, a forbidden abandonment, especially since she spreads abusive talk?

Since you have reconciled with her, make this reconciliation a key to goodness in your relationship with her. Think well of her, but with caution. Advise her gently and kindly. Respond to her wrongdoing with good deeds, for this fosters affection, as Allah Almighty says: "Nor can goodness and evil be equal. Repel (evil) with that which is better: then verily he, between whom and you was hatred, (will become) as though he were your intimate friend." Not inviting her and keeping a distance from her is not considered abandonment as long as you greet her when you see her.