Frank Kogan

here you could say "she offering... he demonstrating" or "with her offering... with him demonstrating": my technical parsing jargon collapses here (skidmore might know); the first -- the one you've used -- seems slightly more fancy and latinate, like a kind of quasi nominative-absolute... however it's not actually absolute in this case because "giles and buffy" and "she and he" refer to the same people

i also feel you could use "her offering... him demonstrating", on the grounds that these are adjectival qualifiers of buffy and giles, respectively, and they're both ruled by "between"