Arthdal Chronicles - this is so amazing drama, so complex, deep, beautiful, so many subjects, great characters, interesting relationships, atmosphere, overall perfection. there are separated tweens, so amazing acting from one actor sometimes you will forget this 2 characters are same actor (good bad tween theme), though this drama should have second season, so it's not ended, but you really should watch it anyway, it is THAT great
Hello Monster (also called "I remember you) GREAT drama and fits perfectly what you want, there are separated siblings, also good one/bad one, relationship and chemistry between brothers are great!!! also this drama has really greatly done really deep and interesting subjects, cast and acting is amazing, music is amazing, only weak part is romance, which isn't main theme, so it even didn't felt missed (I would say FL isn't as good character as everything else in the drama, also I couldn't feel much chemistry, maybe because romance is secondary subject, or because I didn't liked FL, though romance is quite realistic and normal)
Duel also really good drama, interesting, very well acted (one actor plays 2 characters, also good one and bad one) though they are clones, but practically real tweens. bittersweet ending, couldn't say "bad ending"
Are You Human Too? - it's robot as copy of real boy, if it's ok, the story and relationship part would be interesting for you, they first meet when boy is adult and then goes the story
Pinocchio there was what you wanted, tough it's not main theme of the drama
Ja Myung Go also fits, sisters are separated from birth, then they are rivals, they have warm moments too, but mostly rivals - 2 princesses who love one man and have different goals and political views too; also tragic ending.
Who Are You: School 2015 separated tweens but when find out never in bad relationship, also it's school theme and more for young audience
That Winter, The Wind Blows - separated siblings, not rivals or something tough in real they never met, brother dies earlier and his con man friend teaks his place, because sister (FL) is reach, so it's not real siblings, but relationship is like they are long lost brother and sister, but it's slow burn romance, they fall in love, it's quite good romance and amazing acting from ML, if you would interested in story :))
overall N2 and N3 dramas are perfect for you, what you want, N1 also, though it's not ended, they didn't met yet but this drama is so great, you should try anyway, "bad tween" is crazy attractive : https://64.media.tumblr.com/e5cd1c6bf0f1fe3f5f9788b65d0d6d16/tumblr_pu1femKck41wht2r7o4_500.gifv