Silent Hill Heaven

>This doesn't sound like Heather still wanting to kill Claudia.<
No, it doesn't sound like that. But that's picking examples of Alessa and Claudia's childhood, not the emotions she's feeling at this moment. As I've (re)iterated before, she explicitly says, when she finds Claudia's body, that she still intended on killing her herself.

And, as Droo said: If my childhood best friend killed one of my parents, solely with the intention to "fill [my] heart with hatred," I'd probably plan on killing them, too.

Photograph

It's of Dad and me at Christmas.
Looking at this makes me want
to try even harder.

I have to...I can't lose. They killed
my dad and they have to pay for it.

An Item called "Photograph" is in the disc, but not obtainable in the final game. We know the creators decided to name the UFO ending Revenge. Perhaps they couldn't come up with a proper Revenge ending. They may have thought it would be fun to use the name for UFO instead.

If I had to take a guess, viewing this photo continuously would have caused you to add points to a proper Revenge ending in an earlier design. They had such a mechanism in Silent Hill 2, where viewing Mary's photograph deducted points from getting the Maria ending.

A proper Revenge ending would be a bit redundant to the Possessed ending.

I think Heather would have been conflicted had Claudia shown any sign of remorse for what she had done to Harry. Genuine remorse, of course. But since she didn't, she made it very easy for us and Heather to hate her. Heather would have 100% killed Claudia, but even the game itself tells you that's not the path you should follow unless you want the hate to win and for God to be born properly. Heather shouldn't kill Claudia, but that doesn't mean she has to forgive her either.