Yes they love each other though their circumstances won't allow them to be together in the other timeline.
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SPOILER!!
Her mom is the princess who's whole life is focused on surviving the palace and when she gave birth to thie she didn't want her to experience the life she went through and raise her in a dangerous environment so she gave thie to tesetan and left the father and child, since she believes tesetan can give her a more peaceful life.

Does thie's mom and dad love each other? i want the whole family together bruh im a sucker for family stories— also found-family with thie's mercenary group Urgh i love them so much