Is there one where a parent is looking for their child?
So far I haven’t encountered one yet , a parent finding a child is interesting in thought but on paper… well most of them are hidden behind the main plot, and most of them time they end up being the villainess.
Closest thing I've read is probably My Dear Aster where the mom goes back in time but chooses to still marry her bad husband, not for love but because she wanted to see her daughter again.
AND ONE LOOKING FOR BOTH PARENTS
Wait ur so right, the moms actually alive and present in this story, what a rarity
There's a similar one like that, which is "I Only Need the Duke's Child" !! FL travelled back in time too, and married her husband again to have her child back too! Although, i'm not sure if it suits your taste !! (=・ω・=)
This is so cute, first we have a child looking for his mom now we have another looking for her dad it’s sad if you really think about it lol