I think the main difference between Mi-yeong and Rumi's dad and Rumi and Jinu are 2, probably:
1. Rumi and Jinu are each other's first and only love. Mi-yeong and Rumi's dad are each other's last love. Rumi spent her whole life hiding herself, never truly opening up to anyone and focusing on her duty as a hunter. Jinu was too busy starving and then suffering as a demon. Neither of them had the time or energy to have any romantic experience at all. Not even silly crushes. So they're doing anything for the first time and that's why they feel awkward at the beggining before getting comfortable. Mi-yeong and Rumi's father have had experienced romance before, but never in the intensity of their love for one another, but as they had previous experience, they're comfortable with each other right away.
2. Rumi is half demon and Jinu is full demon. Rumi's dad was full demon and Mi-yeong was full human. Because of that, Rumi's father and Mi-yeong had difficulties and faced challenges to build the sense of mutual understanding Rujinu has. Because Rumi helps Jinu remember and regain his humanity and Jinu helps Rumi cope with her demon side. While Mi-yeong and Rumi's dad took longer to achieve this understanding of each other because Rumi's dad might remember a little bit how to be a human, but Mi-yeong will never truly get his demon side, no matter how hard she tries, so all she's able to do is be there for him, which for Rumi's dad is more than enough, but because of it Rujinu can relate to one another, while Rumi's parents can.
Because of those two factors, it's tragic to think about how Rumi's parents are a reverse mirror to Rujinu. Rujinu are soulmates, meant to be. Meanwhile, Rumi's parents were never meant to be. But they still tried to defy all odds, that were all against them, expecting the outcome to be different, even though deep down they both knew they were doomed from the start. That's why I think there's a high possibility of Jinu coming back and Rumi and Jinu's bond to have a lot of parallels to the one of her parents. Rumi and Jinu are the Rumi's parents that made it until the end. Rumi's dad and Mi-yeong that worked. People might say, "it was a bold, original choice to kill the main lead". I would have agreed if it was the right choice. But it wasn't, as I have said why I think so many times before by now
