Emiliano did not get killed in the process of escaping with her. Emiliano got killed because he run back on his own two feet and got killed by Luciano. He was foolish because it was an extremely dangerous situation where Carcel already saved his life not once, but TWICE.
Here is the information in the manhwa where it explicitly said he ran back on his own two feet to die:
https://www.mangago.zone/read-manga/the_broken_ring_this_marriage_will_fail_anyway/uu/br_chapter-103432/pg-4/
About the child, Carcel doesn’t know yet but there is one more chapter left in Bilboa so next chapter.
Also, Emiliano was going to leave Ines. He was going to take the child and leave for a foreign country.
Does carcel knows that she killed her own baby with emiliano,when her family captured her and emiliano got killed in process of escaping with her??? Maybe that's why Inez is being punished by god,because she killed her own baby(though there's a reason why she killed her own baby)