Drama with adult cast.

One More Happy Ending (darn, you've already seen it!)
Another Miss Oh
Just You
A Gentleman's Dignity

Some non-school dramas my mom and I have enjoyed watching together:
Kill Me Heal Me
Signal
Romantic Doctor Teacher Kim
It's Okay That's Love
Misaeng / Incomplete Life
Beautiful Mind
Woman with a Suitcase
Jealousy Incarnate

Thanks for the suggestions everyone! I think I've found some good ones for us to watch together and maybe even some just for me. While I don't mind a little blood in my shows, my mother can be picky about it. I still have no idea how I got her to watch all of City Hunter....It's probably all because of Lee Min Ho. I guess Ji Chang Wook doesn't cut it for her because I just couldn't get her to watch Healer.

pigtails4ever- I haven't actually seen One More Happy Ending yet, it somehow got marked wrong on my list. She might really like that one, so thank you! I was thinking that and Another Miss Oh.

eternalcities- We've watched Full House (thai) together and really enjoyed it, you probably will too!

IzzyDramaLover- Beautiful Life! Such a good drama! I've already watched a lot of the ones you recommended and they're so good. I haven't seen Neko Zamurai yet and it looks amazing! I think I need to watch it now!

Hi FullDex

Having read through the great suggestions above, I would second 'It's okay that's love' and one of my favourites 'The Master's Sun' in particular. 

And to add, here are some other rom-coms you and your mum may enjoy together (with a tad of melo as is usual for most if not all Korean dramas): 

The Greatest Love - with the main cast in their 30's 
Ex-Girlfriend Club - badly underrated laugh out loud
The Lover - quite different from you chaste run of the mill Koran fare, nothing explicit or shocking mind
City Hall - Again main couple in their 30's
I Need Romance - all three are grown up stuff, my favourite being 3
Coffee Prince - the girl is quite young but nobody goes to school, there is an array of handsome men and it is both very funny yet touching
Dal Ja's Spring - mixed cast of mid 20's to mid 30's, funny with the very attractive Lee Min Ki as the main male lead
Lie to me - Male lead in 30's 
Marriage not Dating - they are in their mid to late 20's, really quite funny and grown up
Cunning Single Lady - Male lead in 30's
Heart to Heart - Seriously underrated with some laugh out loud scenes and not shy at all

There are a few more serious non rom-com grown up dramas that I believe your mum and you might like, namely

My Wife is having an Affair
Punch
Secret Love Affair

.... I could go on but the above three are just excellent. 

Enjoy, Luna

I think you'll enjoy Goblin quite a bit. It's very adult, the main girl is in highschool but that's never a focus or anything and I assure you that after watching it, you'll never find a drama good enough. It's a total game changer and I see it's on your PTW list. Give it a go!