Both dramas centre around the marriage of a celebrity. In Papadol! we see an idol marrying a mother with three children whereas in Mukodono! the idol marries into the big family of his beloved. In Papadol! we see the interactions between children and their mother's new husband whereas Mukodono! shows the interactions of our idol/actor with his wife's family and he becoming a part of it.
The original drama from which this one was inspired from, the difference is the idol there is Nakayama Miho.
similar story and premise only gender swaped about a popular woman idol marries a high school teacher and the kids don't like it.