For movies have a look at:
Pained (it made me cry and it was romantic),
Miss Granny (not necessarily emotional or romantic but definitely a good movie for a first timer),
Dancing Queen (it has romance and family love in, it made me cry of happiness) and
Our Heaven (I cried. Plain and simple.)
For dramas I can only think of three right now which are:
Super Daddy Yeol (about a mother, has romance and made me cry. What else do you need?),
Descendants of the Sun (definitely romance and emotional in this one. Plus the editing and scenary is beautiful.) and
Scarlet Heart (not korean but it still was one of my favourites for quite a while, it has romance and very emotional, it is a historical palace setting though so except deaths and betrayal. Plus it's a bit longer then the normal drama. But it's very good.)
I can only think of these which I would recomend to some ones mother xD I probably could think of more but it's past midnight :)