My current Hometown Cha Cha Cha theories, as of episode 6:
A. I theorize that Du-Sik got married and had a baby after graduating from SNU. During that time he only kept in touch with Gam-Ri halmoni. There was an accident/occurrence that resulted in his baby dying (maybe he was busy at work/at his Engineering job and something happened while he wasn't around?). As expected, this tragic occurrence had an extremely negative impact on his marriage, which became strained, and ultimately, he and his wife divorced. Du-Sik came back to Gongjin after the divorce. He has struggled and has yet to fully work through/recover/ move forward from those events because of extreme guilt (when the baby's death might not actually be his fault, but he took on the guilt and feels like it was his fault). So now he lives in Gongjin taking on multiple jobs, serving and helping others as means of coping with his guilt, and also as means of doing things that make him happy instead of having a fancy, high-paying job that took his away from his previous wife and child...and he now goes to therapy regularly in Seoul, as shown in episode 3.
Reasons why I think this is the case for A:
1. I think it's Du-Sik in the photo with the baby and woman. You can see a peek of a guy's hair, and to me, it looks like Du-Sik. He also decided to throw out a black suit in episode 2, and if you recall, the guy in the picture was wearing a black suit.
2. In episode 4, Hye-Jin says how divorce in not a big deal at all and that it is just another decision people make in life, like everything else. Du-Sik quickly agrees with her.
3. Gam-Ri halmoni said she was the only one who kept in touch with Du-Sik during the 5 years he was gone, so it would make sense that she would be the only one who knows what happened to him. Since it was such a sensitive and traumatic time for Du-Sik, the events of that time stay a secret between Gam-Ri halmoni and Du-Sik. However, after so much time, Gam-Ri halmoni was hoping he'd be able to move forward with his life and meet someone new but this has yet to happen (hence, why Gam-Ri halmoni said he can do everything except find a wife....she still wants that for Du-Sik).
4. In episode 2, the townspeople comment how Du-Sikm has been going to Seoul often lately....possibly because he started therapy as per my theory?
5. His child dying and his previous divorce are the reason for his ongoing nightmares.
Maybe now, he's taking small steps in trying to move forward, and maybe all of this is also why, he has initially been so slow and resistant to pursuing a romantic relationship with Hye-Jin.
B. Also, about a possible future storyline development:
1. I think Du-Sik's ex-wife lives in the same building and on the same floor as Hye-Jin's old apartment/apartment building in Seoul.
2. (This one I am less sure about, but it may be possible) At some point, Hye-Jin and Du-Sik ran into each other/interacted at the apartment/apartment building/in Seoul, but Hye-Jin doesn't remember, whereas Du-Sik does.
Reason why I think this is the case for B:
Recall in episode 1, Hye-Jin is talking with the older lady in the elevator, where the older lady said she came to visit her daughter, and then they both get off on the same floor.
I read a theory on Twitter (I tried to look for the link to post it here, but I couldn't find it again) , that it's possible that Du-Sik likely also met Hye-Jin while in Seoul as an adult as well, but maybe she just doesn't remember. The person stated that they thought this was the case because he was rude/dismissive of Hye-Jin from the start when we first see them interacting at the beach in episode 1, and also, when Hye-Jin goes to ask him a question in episode 1 (roughly the 41 minute mark on Netflix), he looks extremely anxious and rubs his neck, but then she only asks to borrow 4000 won for coffee and he seems to relax after that. I'm not sure how likely theory B is (one or even both parts of this theory), but I thought I would throw it in, since I am going off of speculation as it is.
C. What if Du-Sik was the one who organized the fireworks in episode 6?! A small chance of this...a long shot...but still!
Reason why I think this is the case for C:
At the end of episode 6, Du-Sik tells Hye-Jin "I don't befriend just anyone, you know", then the fireworks start and he says "I guess someone got the romance going". Maybe he finally decided that he was going to slowly pursue a romantic relationship with Hye-Jin, hence, he previously commented to her in episode 6 about how she should comfortably cross the line with him...and so he started off his slow pursuit with fireworks?! Could it be?
D. It's clearly obvious that there is some kind of underlying romantic relationship and history/backstory between Hwa Jeong and the teacher who returned to Gongjin (I can't remember her name at the moment). Therefore, I believe Hwa Jeong and Yeong Guk divorced because Hwa Jeong realized she could no longer be married to a man, but it remains a secret between them because they both do not want anyone in the town finding out for the sake of their son. They want their son to grow up without people gossiping about it even more.
It's a really great show and I look forward to it every week! Each episode always puts a smile on my face and makes me laugh at some point. It's a great find, especially because I didn't think it would be this great when I watched the trailer, but I really love the show! :)