So, just in case...
#1) My memory is that the book had a red dragon on the cover, a heraldic style one, and I think the dragon may have been Welsh, but I could be wrong. It was about a little dragon who lived with a family, and ate coal. But winter comes along, and coal gets very expensive, and they don't have enough for the dragon, so it gets very weak, and the kids are very worried.
Here's where it starts to sound like I'm on a crack, because I swear, in my memory, the kids hear about a miracle fuel that's being used by the government, and somehow--I think trains may get involved--they wind up smuggling the dragon into some kind of government facility (possibly a train) and feeding him bars of uranium. There's a happy ending, I think the dragon gets a job running a boiler or the stoking the steam train or some kind of government job, but I have a really clear memory that at one point, the dragon gets fed bars of uranium, which is the sort of freaky logical thinking that makes a real impression when you're a kid.
I would have read this in the early eighties, and I'm not sure how old it may have actually been, but I would like to find it again just to prove to myself that I'm not crazy about the uranium bit.
Someone on the LJ find_a_book community said they remembered having read it, but couldn't remember the title either, so possibly I did not hallucinate its existence.
GLORY BE, located! Thank you so much--it's Tecwyn, last of the Welsh Dragons! Eeee!
#2) There's a girl who winds up alone in a cabin in the woods. (It might be a somewhat enchanted woods, or it might not. I don't recall a lot of magic, but I also don't recall its lack.) I want to say that she's following in the footsteps of her father or grandfather, who may or may not be dead, and reading his diary, but I'm not entirely clear on that bit. What I recall most clearly is that she's living alone in this cabin, doing all the things she needs to, and she doesn't really want to be found by the outside world. ( I get the feeling it was a little over my reading level, on the whole motivation front...)
There is a family of mountain goats that she watches. I'm very clear on the existence of mountain goats, because the baby is called "Billy the Kid" which I thought was the most clever pun I'd ever read at the time. All the other details may be wonky, but the mountain goats are solid. If it doesn't have mountain goats, it's not the book I'm after.
This would have been the early-to-mid-eighties. It most definitely is not The Secret Garden. (I ordered Mandy on the off-chance...) In feel, it almost reminds me of Valley of Horses, completely the wrong setting and era, but same girl alone watching animals kinda vibe, only without the Cro-Magnon sex at the end.
If anybody successfully names either one of these, I will be terribly terribly grateful.