So recently I've been able to convince my mum to watch a drama with me! I've been watching for years but every time I've asked her to watch something with me, she said "Sure~ Later okay?" but yeah, we never went through with it. A little over a month ago, I talked about Weight Lifting Fairy Kim Bok Joo so much that she agreed to watch it with me. And then, the same thing happened to her that happens to all drama fans- she got addicted! As soon as we completed a drama she asked me about the next one. So far we've watched WFKBJ, Hana Kimi, Full House and Kiss Me and now I'm running out of ideas. I've watched my fair share of dramas (quite a few are not on my lists) but I'm just lost as to what dramas I could make her watch next... If anyone has suggestions, it would be awesome!

We like rom coms with drama but not over the top melodrama, action and sci-fi are good, too. Actually any genres are okay but I'd like to avoid heavy, complicated and political plots for now, she isn't too used to fast subs and political and cultural settings yet (so avoid things like W and The K2). Also sad endings are a no-no. It doesn't have to be recent, old dramas are awesome.

For now I was thinking of Shopping King Louis, Another Miss Oh and Healer, those are beginner mum friendly, right?

All help is appreciated, thank you!

Another Miss Oh is very melo and sad and Healer is action-heavy LOL

how about - Reply series, It's Okay That's Love, Fated to Love You, Oh My Ghost, Oh My Venus, She Was Pretty, Lucky Romance
J-dorama: Family's Form, Jimi ni Sugoi, Juhan Shuttai, Kekkon Dekinai Otoko, Kounodori (this one she will love)
I like your choices, especially Another Miss Oh because it's hilarious and Shopping King Louis because it's adorable! I would also recommend It's Okay That's Love, I Hear Your Voice (but beware, this one is noona romance), Age of Youth (it's about girls in their 20s, but I'm sure your mother will be reminded of her youth haha), Marriage Not Dating is hilarious too so it could be a good choice.
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).
I hope you'd enjoy these with your mom. :)
Shopping King Louis- most adorable drama out there
Good Doctor- since the main character is mentally-challenged yet was very loving to his patients
Pinocchio- reveals what the media hide from the public; female lead has a troubled relationship with her mom
The Girl Who Sees Scents- very suspenseful yet fine to watch with mom
You Who Came from the Star- laugh and cry with your mom

I don't suggest watching the following with your mom :(
Oh My Venus- too much romance unless you're comfortable to watch it with your mom
Another Miss Oh- characters are too wild in romance
Wow thanks to all of you for aall these suggestions, they're gonna keep her going for quite a while haha
And a lot of them are already on my ptw so that's great! 
Thanks again, wish I could give you all a cookie or something :) ^.^
I always though that if i were to show a k drama to my mum it would definitely be Reply 1988. it has good balance of romance and believable slice of life stories plus it might be interestesting for her to watch how different were late 1980's in korea compared to my countrys :D
wakamono tachi
5-ji Kara 9-ji Made
Family's Form
Good Partner
Mou Ichido Kimi ni, Propose  
Nagareboshi
Saikou no Rikon
Sunao ni Narenakute
Tsuki no Koibito
egg-mont - The Reply series is definitely a drama I want to watch at some point so I added it to my list. Should I start with Reply 1997 though since it came out before 1988?

yukitomo - Thank you, you gave me some really nice ones and even helped me find one I was looking for! :)
Shopping King Louis is a good choice, likewise with Healer.

Others I'd recommend are:

Reply series (Reply 1997, 1994, 1988 but you can watch in any order)
Suspicious Partner (still ongoing)
Rooftop Prince (slightly political as it's a historical time-jump drama but it's a really fun watch with plenty of sweet/hilarious moments - this was the first drama I convinced my dad to watch with me and he enjoyed it a lot despite not being big on dramas in general)
Strong Woman Do Bong Soon
Protect the Boss
Tunnel
Okay then I guess I'll start with the Reply that appeals to me the most.
Suspicious Partner is on my PTW but a 40 episodes drama might be a bit much for her right now haha
Rooftop Prince looks interesting, I do like time travel plots so I'll watch with her when she'll be a bit more used to dramas.
As for Protect the Boss, is it the arrogant chaebol-ordinary girl story line? If it is, then I don't know about that haha
Tunnel- Assuming you're talking about this Tunnel, it does seem interesting, we're pretty into detective shows so it appeals to me. But is it a sad ending?
Suspicious Partner is split into 40 episodes that are 30 mins long each because of advertisements in-between, so it actually works out as the same length of a 20 episode drama in total, but you could also wait and see how you feel when the series ends haha (just watch out for spoilers!)

Without spoiling too much, Tunnel's ending in my opinion was pretty satisfying, though it left some and a bittersweet one with positive/good outcomes outweighing the bad ones. I'd also recommend Signal if you're into detective plots, as it's pretty similar to Tunnel.
Goblin is pretty mom friendly.