• bandhuḥ — a relative / friend
  From √bandh, 'to bind.' Family is a binding — a kind of dharma-bond. Gauḍīyas note: only the kṛṣṇa-bandhuhood is unconditional; worldly bandhutva can be loosened (cf. BG 9.32, 9.33). Balarāma works within worldly bandhutva to make the higher one possible.
• tyājyaḥ — to be cast out
  Gerundive of √tyaj. The same root as 'sarva-dharmān parityajya' (BG 18.66). Cast out from family ≠ cast out from God. Balarāma's lesser tyāga sets the stage for the greater.
• doṣaḥ — fault / wrongdoing
  From √duṣ. Doṣa is the technical term in dharma-śāstra for an act that incurs prāyaścitta. Balarāma names Rukmī's doṣa to make Rukmiṇī accept that her brother has not been treated unfairly.
• hataḥ — killed
  Past participle of √han. Balarāma's pithy reasoning: 'He has already been killed by his own sin — why kill him again?' This is the chapter's clearest articulation of karma as auto-execution.
• vadha-arha — deserving of being killed
  Vadha (killing) + arha (deserving). The compound that the dharma-śāstras use for capital offenses. Balarāma admits Rukmī technically belongs to this class — then immediately commutes the sentence by appeal to relation. Justice tempered by family-mercy.

• Where do you redo what karma has already accomplished against an opponent?
• Could removing from intimacy be sufficient rather than killing the relationship?

A relative who has earned death by his deed should be cast out, not killed — like a diseased branch pruned, not the whole orchard burned. Balarāma articulates a careful dharma: there is a level of family-protection that survives even the gravest wrongdoing.