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Oh, they get lots of time with their kids. In fact, they even live to see their grandson become the emperor. The side story ends with Ines 9 months pregnant with their third child and Ines and Carcel holding hands and promising that they will walk side by side from now until 100 years later until they die at the same time and enter eternity together. That’s the author telling the reader that Carcel and Ines will die at the same time again just like they died at the same time in the first timeline.
The author thoroughly completed this story. After the end of the side story, the author gave a list of events that occurred decades in the future. That’s how we know what their third child is like. He’s exactly like Carcel in almost every way. Their daughter became empress and their first son married Enrique’s daughter and he was his sister’s strongest political supporter. Ines and Carcel stayed out of politics so their first son did the political work.
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Ines died from illness and Carcel died on the battlefield during war. In fact, Ines died because Carcel died. Why? Because Ines told the priest at her bedside that if Carcel died, she wanted to die. The priest, who was really Anastasio, granted her wish. Therefore, when Carcel died on the battlefield, Ines immediately died at the same moment. Since this precedent has already occurred, if Ines and Carcel pray to die at the same time, their wish can be granted by God. It’s already considered done by the way they affirm this in the last words of the side story.
Regarding the other lives, as Ines said during the Mendoza arc, Carcel was always alive when she died. Since Ines was walking a different path, there’s no way they would die at the same time especially since Ines committed suicide.

All of Carcel’s lives so far ended with his unfated death. Carcel doesn’t know it but he made wishes with Anastasio after every single death. All but one of his wishes were made for Ines’s wellbeing. The one wish that wasn’t about Ines was about himself. He made the wish that he would never love anyone else but her.
So current day Carcel wishing he can meet Anastasio has already been fulfilled. It’s just that Ines has free will so Carcel’s wishes cannot override her free will. Nevertheless, all of Carcel’s wishes for Ines will be fulfilled in this current timeline and all of Ines’s wishes that she made for Carcel in the first true timeline will be fulfilled in this final timeline. Both will meet their TRUE deaths and this will finally release them from the repeated lives. The world must go forward and their descendants must carry on. It’s also Ines’s fervent wish to rest eternally with her husband after this final life.