The first, I'm really liking and looking forward to more is about a woman who marries the prince, but is unhappy, becomes nasty and disruptive and in the end gets not only herself but her family killed. She did not mean to get her family killed and regrets here action in death. Current day, she is reincarnated, becomes a surgeon to make amends. She becomes one of the best, but dies in a plane crash and ends up being reincarnated as her former self before her marriage. She decides to break off the wedding but the king does not want this. As deal she goes to work at a hospital and starts saving people. She has to make a significant contribution to the kingdom or marry the prince. I'm enjoying it quite a bit but unfortunately didn't bookmark it / add to iist.
The other is an isekai with summoning but slightly different then many. A queen has to marry and have a child but there is no one she wants. She decides to summon this guy because he meets certain requirements. When he is brought over he is actually given the choice to stay or not. He is told that if he wants he can have minimal responsibilities. He stays, marries her and they actually become a real couple. It is mix of some minor politics, ex: he is given a gift at a party and depending on how he responds will possibly create a political debt. Focuses more on the interactions of being married into royalty. It is different in there are no huge battles and other stuff. It is actually pretty good because of the difference isekai story line for a change. There is magic but not over the top. Again didn't bookmark / add to the list and can't find it now.
If someone here knows the names, I think you would like both.