I'm pretty sure Sei has NOT forgiven the prince. She forgave the king.
The main issue here is that after spending time here, Sei has met many very considerate and caring people. She's formed bonds with them-and consequentially with this world and kingdom. It would be unreasonably spiteful to hurt the country just because one guy from there is a jackass.
As for rewards...yeah, she could probably ask for more, but she's generally left in want of nothing and as an otherworlder, it's not like there's any grand ambition for her to pursue besides living a peaceful daily life. A little lacking in ambition, but people without drive or initiative exist in the real world too.