My favorite example of established relationships are where you get to choose the relationship with the character. The Odessa Dating Games with Odi/Odanna and Wayhaven Chronicles with both your mother and Bobby are the only examples I can think of right now. I also really enjoyed being able to change the relationship with your mother as the story went on. Some characters you end up disliking after getting to know them, so it’s nice that you don’t have to stick with a certain relationship. Plus, I generally just enjoy relationships that grow and change over time.
I wouldn’t say that I dislike established relationships where you don’t get an option to define the relationship, but the characters always seem far less impactful to me when I don’t have the option. It could be a coincidence of writing or characters I just didn’t enjoy, but that’s just my thoughts on it. The only example I can think of that I enjoyed an established relationship was with Jun/Junko in Samurai of Hyuga, but you also get options to define your feelings and relationship with them as the story goes on, so that could have deepened my enjoyment of interacting with the character.