Prodigal son drama/ movie (don't know if it's been posted before)

well the now airing ''moon river'' is one. Dunno if they are gonna make up yet but I bet they do.

Also I Miss You. I don't remember if they make up tbh 

I don't remember any drama with that main theme, but in the following titles there's a bit of it...

Romantic Princess (leaves home when his love for the female lead isn't approved)
Majo no Jouken (same reason)
Heart to Heart (the same as before, but for a shorter time)

The Best Future (starts when he already left home; since it's a short web drama, this theme isn't very present)

Legendary Witch (in the flashbacks they let us see why the female lead's husband left the house and how he reconciled with his father; he's not the male lead, but at some point, his step-brother stop living with his mother and near the end of the drama they reconcile)

Dear Sister (she suddenly left the house after graduating; the drama starts when she returns and decides to live with her sister)

You're welcome and, don't worry! I was being prudent because it's been a long time since I watched Smiling Pasta and I don't remember there was a part like that (I just remember there was a part when her father made the pasta, nothing else :/ )... so I wasn't sure. >_<

I guess I didn't give it too much attention and/or I need to re-watch it... @_@

Just finished witches romance and that has a 'leaving home' theme to it with Romance in it (hot!). Very good and fits your description although it wasn't parents per se .. just his dad.