My early hiking memories were one of two things: either Boy Scouts or parents. If it was Boy Scouts, it was a bunch of 13 year old assholes wearing cotton socks, blue jeans, those tan shirts, and a plastic rain poncho (because somehow it was always raining). I didn't know proper rain gear was an actual thing until years later. And we always car camped, so they were the same bland trails every other car camper walked down. If it was parents, they definitely weren't getting along, not arguing but neither happy with anything in life or in that day. Kids see that attitude as clear as day. It was fifteen years before I did it on my own terms and found I liked it. I also learned that nothing we did in Boy Scouts was relevant to backpacking. As an aside, I see in my niece what I think I experienced as a child: parents disappointed with life and a child who tries to make them happier (but can't). I don't know what to do about that.
Something that might help is just being there to remind her that her emotions/self/life and all that deserve her attention as well. She’ll realistically keep trying to take their problems on herself but at least there will be another voice in her head telling her she matters too/ is her own person. Literally just talk to her about her day, if she shows interest in something encourage that and maybe gift her something small to help her progress. I can pick out other peoples emotions with relative ease, but when it comes to my own I need to remind myself to pay attention by keeping a journal. I’ll bet I still would have issues if I had somebody like that, but they wouldn’t be as bad.
We'd go hiking up Caballo the hard way - up through Rendija. It was fifteen miles one way because of road closures. We'd often see our friends the Boy Scouts coming down the other looking chipper - because they'd break trail (this trail, in fact) and do it the pussy way. I used to feel left out because my father was adamant that his son would have nothing to do with "those paramilitary Nazis." Then I found out that the Scouts were pussies and it didn't suck so hard. "You were always such a happy baby," my father said, upon me showing him a picture I found in my dead grandparents' stash. He looked wistful. It wasn't until I dug through the rest of the photos - in the process of going through my parents' slides of my first five or six years, I watched the progression. By the time I was two I was a haunted-eyed little kid whose back was always to the camera, unless I was cornered like a wounded animal. There are legitimately no photos of me between the ages of eight and about sixth grade. To date, my proudest accomplishment is how bubbly and joyful my own kid is. She's irrepressible. She wakes up happy, she goes to bed happy, and in the middle she's almost entirely happy. I watch her and wonder at exactly what kind of terrible fucking parent you have to be to kill that so thoroughly. I don't know what to do about it either. But I know it affects me so much more to see it happen to someone else than it did to know it happened to me.
You should absolutely be proud of yourself for having a happy child. I'm happy she's happy, and I'm happy you know she's happy. The world is a better place.