• nyamantrayetām — they both invited
  Imperfect dual middle of ni + √mantr (to invite, to advise). The dual is the verse's secret: two persons act as one in inviting Bhagavān. Gauḍīyas read it as the unity of bhakti — different stations, identical bhāva.
• yugapat — simultaneously
  Adverb: 'at the same moment.' This word is the hinge for v. 26 — only yugapat invitations could give Kṛṣṇa the occasion for His yugapat presence. The bhaktas' synchronicity is the cue Bhagavān has been waiting for.
• ātithyena — to be their guest
  Instrumental of ātithya (hospitality). The host-guest relation is, in the Vedas, the model of dharma between unequals. By accepting both invitations, Kṛṣṇa formalizes equal honor to king and to poor brāhmaṇa.
• dāśārham — Kṛṣṇa, the descendant of Daśārha
  From Daśārha — an ancestor of the Yadu line. The dynastic epithet is used here precisely because the verse is about Kṛṣṇa's family-side identity entering both homes as kin. Bhagavān is invoked as 'one of us' by both bhaktas.

• What synchronicity have I dismissed as coincidence that was actually grace?
• Where could noticing simultaneity sharpen my recognition of divine arrangement?

Two invitations rise into the air simultaneously — one from a palace, one from a hut. The Lord must answer both. Kṛṣṇa's first solution is no human's solution: He goes to both, at once, fully, in each.