Spoilers: Oddly enough, it is not necessary that you end every date with a "good" status in order to achieve a character's good ending. Instead, you must at least complete the character's 4th scene (which makes them available for the final scene) and perform some task specific to the character.
In Remy's case, he has to adopt Vara (the pink flyer dragon that passes you by on the first day). In order to do this, you need to examine Remy's photographs when at his house for dinner (they can be examined three times, I think only once or twice is enough and maybe discussing them with Remy immediately afterward; this step is properly fulfilled if a photo frame icon becomes visible on the status screen, next to the other item icons) and save Vara (which involves visiting the grocery store when it becomes available for the second time and then deciding to follow Vara after she leaves the store).
If you completed the previous two steps, then during your third meeting with Remy, an option with a picture frame icon next to it will become available, where you suggest to Remy that he connect with Adine and adopt a kid (Vara).
If you visit the hatchery afterward and Remy appears during the scene with Adine, you have succeeded and the good ending should trigger if you select him for the final scene.