Oh... ok. Well, that was surprising. I thought it was a simple hug.

me too

I'm trying to make sense of how this picture happened... and I'm not sure how it happened. How'd the gohei go through Remilia's back, and then somehow end up in Reimu's temple?

Remilia got hit in the back, then went to give Reimu a hug. Either:
-She purposely got it in Reimu's face thusly, or
-The blood on Reimu's face is just Remi's.

Reimu stabbed Remilia with her gohei. Remilia is stabbing her back.