If you loved Princess from the Moon, try Time Traveller: The Girl Who Leapt Through Time
A bridge between a film you've already seen and one most people haven't. Here's what they share, and what the second one does that the first one doesn't.
You already loved

Princess from the Moon
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Time Traveller: The Girl Who Leapt Through Time
What they share
Theyboth carry the bittersweet, tender mood tags, and they sit in Adventure / Science Fiction territory. If that's the register that drew you to Princess from the Moon, the second film will land in a comparable space — through a different lens.
bittersweettender
What Time Traveller: The Girl Who Leapt Through Time is
Peggy Sue Got Married if Peggy Sue could time-travel for others. A young woman travels back to the early 1970s to fulfill a mysterious wish of her injured mother. It's a sweet if minor variation on a familiar theme.