स वै न शक्नोमि पितुः प्रतिज्ञामिमामकर्तुं सकलां यथावत्॥
स ह्यावयोस्तात गुरुर्नियोगे देव्याश्च भर्ता स गतिः स धर्मः॥
sa vai na śaknomi pituḥ pratijñām
imām akartuṁ sakalāṁ yathāvat
sa hy āvayos tāta-gurur niyoge
devyāś ca bhartā sa gatiḥ sa dharmaḥ
saḥ vai na śaknomi = I cannot; pituḥ = My father’s; pratijñām imām = promise; akartum = not fulfill; sakalām = fully; yathāvat = and properly; saḥ hi = he; āvayoḥ = of both of Us; tāta-guruḥ = is the father and competent; niyoge = to appoint [any one of Us as the crown prince]; devyāḥ = of Queen Kausalyā; ca = also; bhartā = he is the husband; saḥ = he; gatiḥ = is our shelter; saḥ dharmaḥ = and the means to attain benefits in Our afterlife.
I cannot not fulfill My father’s promise fully and properly. He is the father of both of Us and competent to appoint [any one of Us as the crown prince]. He is also the husband of Queen Kausalyā. He is our shelter and the means to attain benefits in Our afterlife.
Lord Rāmacandra is a mild person. He could not refrain from fulfilling His father’s promise that Bharata would be coronated and that He would be exiled. In other words, He would certainly fulfill His father’s promise. Why? Because His father was competent to appoint Rāma or Bharata as the crown prince. Since He is the husband of Queen Kausalyā, she should not transgress his orders too.
NOTE. Generally, in societies that followed Vedic dharma, the king would hand over the kingdom to his eldest son of his seniormost queen. But there were exceptions, one of which is noted in Śrīmad-Bhāgavatam 9.19.23:
bhū-maṇḍalasya sarvasya pūrum arhattamaṁ viśām
abhiṣicyāgrajāṁs tasya vaśe sthāpya vanaṁ yayau
“Yayāti enthroned his youngest son, Pūru, as the emperor of the entire world and the proprietor of all its riches, and he placed all the other sons, who were older than Pūru, under Pūru’s control.”
Therefore, Lord Rāma has noted here that His father is competent as per Vedic dharma to appoint Him or Bharata as the crown prince.