silverspoonzie this might be a long shot but dragon mania legends? I don't remember a dragon named molly, I think you name dragons in it yourself, but I believe it had something like a flute in the soundtrack for the majority of the time. There's a newer version, but the old one had less quality graphics, I don't know when it was updated into the new version. You had a team of dragons in it and fought other dragons, especially for the main quest. There were water/blue dragons and fire dragons I know for sure at the time and you could breed new ones but that's all I remember from it.
Dragon story could be another option, I don't recall much of that game at all but I'm throwing it out there anyway.
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Its been in the back of my mind for literally years but I used to play this game, browser based I believe, on my laptop. You played as a stick figure and went through different levels of a game, and it was pretty simple. Mainly black and grey I think. The objective each level was to get a key and "escape". The stick figure was just plain black, no unique design or anything. The key was just a floating key, nothing special. My friend also remembers playing it and so does my dad but none of us remember the name, or if it even exists now lol. During the level, the walls and layout would change. So like if you walked to the left wall, the screen would turn so you'd be walking on that wall but it looked like the floor since it turned. I remember there being a lot of spikes you'd have to avoid, I think they were light grey/silver.Â
I know for sure it's not the game shift.
Another thing I've been trying to remember is a series of animated short stories I saw years ago. It was not for children but I saw my parents watching it one night. It had a really unique animation style, similar to claymation probably, but it might have just been 2d. One of the stories I remember a lady was on a train and was having heart issues, or like, her heart came out of her chest, but I may have smashed together some of the scenes in my head since then. I remember one scene with a couple sitting in what I think was a waiting room. Not much to go off of at all, ik, but thought it would be worth a shot. A lot of the stories in it were dark, but the colors used were more vibrant in contrast to that.