IAnother Miss Oh isn't too much of a melodrama, it could be a good one.
I don't have many indications on your Mom's taste, but I would recommend:
Let's Eat - nice adult romance... and food!! With a little luck, she will cook some delicious meal after that.
Jealousy Incarnate - I'm surprised no one suggested it. More adult characters and great character dynamics.
Ms. Temper & Nam Jung Gi - great drama, a little low on the romance side, but the office plot (keeping the company afloat) and the family part are great. Plus it had a little feminist vibe.
Queen of Mystery - Romance isn't very present (although chemistry between the leads is amazing), the crime part is good.
Witch's Romance - Cute and funny romance, great side characters...
Wild Romance - It's worth a shot, it's both hilarious and quite dark, but it balances very well (when it could have been a total miss). Far less stupid that the synopsis lets you think, it has an actual plot.
38 Task Force - If you want some fun action and an amazing set of mismatched characters (blink and you'll miss the romance though)
City Hall - It might be a good point of entry to start political drama, it's light on politics, but you get to understand how the whole South Korean political system works.
My Lovely Sam Soon - Since you're not afraid of older drama, I found it very funny and very cute.
Coffee Prince - Everyone should see it, right?
Like immortalcupcake said,
It's Okay, That's Love is a good one.
Oh My Ghost is quite good too (was my first kdrama actually).