Right now I remember:
Five Enough
Marriage Contract
Glorious Day
Bad Family - it fits your wishes, but it has never been on Viki, it’s an old one.
Gloria - the drama might have had his up and downs but the “family feels” were just good. No longer at Viki
Oh, I’m watching one of those right now:
Somewhat Family (also called “Unexpected Family” (어떻게 든 가족)
The story of a married couple, Sung Dong-il and Jin Hee-kyung, who run a boarding house near the airport and live with various people who work at said airport.
And another one on my watch list:
Be My Dream Family (Other names: Dreams Even if Behind; Dream Even though Tricked; A Fool’s Dream; Dreams of Belief; Sokado Ggumgyeol; In My Wildest Dreams)
The story of two families of different cultures meeting in the twilight of their parents and becoming one family.
And one shouldn’t forget
It’s okay, that’s Love
Interesting thread, but you mention a lot of good ones. I have to think about it hehe
Kimchi Family
Heard it Through the Grapevine
Best Wedding - not at Viki
Beyond the Clouds - no longer at Viki
Family’s Honor - an old one, no longer at Viki
Fantastic - one I love especially because of the mood it gives you is just so good, at least for me, but it’s not an easy watch.
What happens to my family? - It starts out not so heartwarming, because the father sues his adult children for never paying attention to him/taking him for granted, but you’ll soon find out why and his children do change for the better.
My father is strange - A seemingly typical family consisting of parents and 4 children. One day, an idol-turned-actor shows up and claims he is the biological son of the father.
Wow, thanks for all the reccs! 
A lot of them seem like weekend dramas, though… are they all worth the loooong watch?
Well, the dramas I recommend are 
Plus I also really liked It’s okay, that’s loved and Fantastic. (I was the Dutch mod for both What happens to my family and Fantastic)
If you’re not sure you could check out the trailer on MDL and then decide if you want to watch it.
Well, about weekend dramas that’s the trope of them - being heartwarming, most of them at least.
There was also
Legendary Witch - I think it’s also no longer on Viki
You know I think “Wok of Love” with the Bromance and Gangsta “family” I love it.
Coffee Prince - The “family” of guys at the coffee shop were so Awesome
A Gentleman’s Dignity (but that is older guys) they are a group of friends I love their interactions
probably not one you would like
Crash Landing on You - of course the “Squad” was the best family ever
Goblin - Of course the friendship Bromance and the nephew
Oh My Venus - the three guy friends and her together
Oh My Ghostess - the “restaurant” family and the chef takes care of them
Another Oh Hae Young - All kinds of misfits
Beauty Inside - I loved the family/friend dynamic with supernatural going on
DOOM - I love how they all made up a family together - including co workers
And yes - Your 30 but 17 because I loved the housekeeper so much!!!
These probably aren’t what you are talking about but I guess I don’t watch a lot of family drama more like misfits that become a family.
Quess who is in Another Oh Hae Young!!!
More of an adult role but I love her.
I don’t watch very many young shows. I love “Spring Is Green” and the friendships that are growing, the family of the main lead is AWFUL just AWFUL - he needs his friendship family
So many already got mentioned. Let me think…
Move to heaven 
Off the top of my head: Racket Boys on Ntflx. I just finished it. So much better than I ever could have anticipated. There’s a whole combination of an actual family who take in a whole bunch of other kids that they are coaching on a rural badminton team, and then the whole rural town also plays a ‘family role’ with these kids.
When I started to think about this, and peruse my collections for more ideas, I realized that I must be drawn to this ‘trope’ as well, because there is an element of this ‘found family’, to some extent, in nearly all of my favorite dramas.
Some of the more obvious that haven’t already been mentioned:
Melo is My Nature
Flower Boy Next Door
The Imperial Coroner and Maiden Holmes with their sleuthing teams
Happy Once Again
Bromance - Both their families are lovely
Best Lover (not on Viki) - contract marriage trope
Love Now - long, definite angst, bittersweet ending
Inborn Pair - another very long one, arranged marriage, they live with his family.
10
villarrealsisterslov_182
31 Dec 2017
381
I Honestly Loved This Drama I’ve Rewatched it Maybe three Or Two Times I Only watched it only becuase of iu but I love the romatic story Lines Between the Couples i love IU’s acting i think she should be acting in more roles shes so enjoyable to watch in my Opinion i Just Love Everything. i love how it slowly draws you in theres somethings that annoys me about the drama but it was mostly little things like(Sometimes slowpaste i sometimes hated iu’s real mom but then i wished there mother -daughter relationship grow more) i loved how iu and her Real-LIfe best friend Played Sister Are on here. i think i liked how he liked her first thats what i liked most i hate when the girl is so desprate as the female lead i like it when the guy gives into hes feelings first it just shows how much he really likes here idk maybe just me any way yeah thats it. (sorry for missed spelled words for all those spelling correcters out there im currently sleepy and excited from finishing yet another all day nighter till next day drama yall get it anyway thats my review
You asked, 
and we answered! Now get yourself some snax, and snacks. Settle in for the ride in drama land!
Ok, this is my first list for this:
Angel eyes, I love how his family “adopts” her and treats her like a part of the family.
Another Miss Oh, not just with his siblings but with his team.
Go Ahead, if we talk about families, the list will always include this drama.
Hospital playlist, they look like a family for me
Lovestruck in the city
Mystic pop up bar they are a family indeed, but they didn’t know it
Taxi driver, I love their friendship and supportive relationship
YES! This is also what I wanted! I just didn’t know how to explain it so I wrote “unexpected family” 
Thank you!
Thank you! I forgot all about Imperial Coroner! 
Thank you!
I’ll have to learn not to binge and just… enjoooooy the ride
This one is on my watchlist!
All right, I’ll start on a weekend drama. I can’t choose, though:
Well, if you want to go for a weekend drama you would need to let this one out of the pot, since it is a “normal” 16 ep drama. Although I would love you to watch it, since it is one of my favorits.
Let’s see what other weekend drama could replace it. Oh, there is
Five Enough, a woman with 3 kids and a guy with 2 kids fall in love with each other, and have to find a way to create their new family, with the extensions of one grandmother living with her, and he was living with his in-laws and sister-in-law since his wife’s death, as well as her kids’ dad.
Smile, You, it is a shame it is no longer at Viki, it was really funny, about a former well off family moving in with the ex-chauffeur’s family and the son of the former well off family slowly falling for the other family’s youngest daughter. When the 2 families find out their relation ship it goes berserk, since they just don’t really want to be in-laws. Epic the morning exercises invented by grandpa and everyone living in his house has to do it.
Marry Me Now, and as far as it comes to emotions, this might be the closest you can get to Fantastic. Former youth sweethearts meet again and fall in love again in their 60’s.
Love Now and Inborn Pair are both from Taiwan I think, not fitting the usual 50 ep criteria for a K-drama, so I would not recommend it for this challenge.
Legendary Witch, but don’t know if you can find it anywhere. About a rich family’s daughter-in-law with a poor background, getting pushed out of the family, when her husband goes missing and is supposed to be dead. She gets to take the blame for some forged financial numbers in the company of her in-laws and has to go to jail because of it. In jail, she makes some friends with whom she will open a bakery once they made it out, and she finds a new love, not that her ex-in-laws want to tolerate that.
Glorious Day, has the typical bad or worst encounter possible of the FL and the ML, it pretty much is what you would call a traditional Korean weekend drama, except some characters do not act that way.
Angel Eyes, has a lot of warmth to come up with and a lot of heartache, but well tissues at place, for a girl that was kind of adopted by her boyfriend’s family, she was blind and fate had it that his mother was killed in an accident and her … You can guess the rest, fate had it that their ways separated. Many years later, she can now see thanks to an operation, they meet again and get a 2nd chance, even she has a new boyfriend and her father is against the relationship.