I think that the first prince is his brother's child and that she cheated on him while they were in the relationship and she returned just so she could take revenge on the king because he became king not his brother
Comment by Loly on I Won’t Accept Your Regrets - Chapter 71
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Also thinking the same about her child being his brothers child, but maybe moreso taking revenge for not having the power to keep her in the empire and choosing to marry someone else while her life was however bad it was as a concubine in another land... especially so seeing he doesn't have feelings for her upon her return, nor showing much feelings for their "son" in comparison to Eli