In plain words
Daśaratha had three wives: Kausalyā, Sumitrā and Kaikeyī. A daughter was born to Kausalyā. Her name was Śāntā. Daśaratha gave her in adoption to a king. After that, no children came to him again. This is how the family Dharma of those days stood: one must not marry a second time without the wife's consent. Then Daśaratha asked Kausalyā's consent to marry Sumitrā. She gladly agreed.
Sumitrā, true to her name, had a most pure heart. When she too bore no children, Daśaratha went to the king of Kekaya and asked him to give him his daughter in marriage. The kingdom of Kekaya means the land of Kashmir. The king of Kekaya: “Daśaratha! You have two wives. Now you are asking for a third wife. What for? Surely because you want a son to rule the kingdom! Then will you give the kingdom only to the son born to my daughter?” he asked. Then Daśaratha came back to Ayodhyā: “The king of Kekaya has laid down the condition that the crown must go only to the son to be born to Kaikā. Is this agreeable to you both?” he asked Kausalyā and Sumitrā. They agreed most gladly. “For a son to be born to you and rule the kingdom: that alone is joy to us,” they said. Then Daśaratha promised the king of Kekaya that he would crown only the son to be born to Kaikā, married her and came home. When she too bore no children, he performed the Putrakāmeṣṭi sacrifice.
Then the Yajña Puruṣa appeared, handed Daśaratha a vessel of pāyasam and told him to share it equally among his three wives. Daśaratha put the vessel into the priest's hand and through him gave it equally to all three. Kausalyā was very glad. For: “I myself am the chief queen. So the kingdom will come to my son alone,” was her thought. Kaikā too was very glad that by the promise Daśaratha had given at the time of the wedding, her own son would be crowned king. But Sumitrā knew that the son to be born to her had no such chance.