Same age gap as mine, OP. They, too, would fight over thin air (still do, and DC1 is technically an adult now).
When they were younger, I used to make sure DC2 was in bed before DC1. That way, DC1 had half an hour of guaranteed time just with me/us.
DC1 was prone to lash out, and DC2 knew this from a very young age. XH and I used to call it "pesting". Many, many times did I remove her before it got to the hitting and meltdown stage (didn't always, as it sometimes happened too quickly).
Is there any way you can ensure your DD has a bit of physical and emotional space from her brother on a regular basis? I know it's hard when they are both small enough to need you around pretty much all the time - but even if you just pick up DS and move him away from DD every time he looks set to encroach on her space in a negative way it would give him the message that he needs to leave her alone, and it would give her the message that you're taking her needs seriously.
I disagree with PP who said that Father Christmas removing presents teaches them that actions have consequences. No it doesn't. It teaches them that adults apparently do really random and bewildering and unfair things.
The only natural consequence to a child using a toy/cup/whatever as a weapon is to remove said toy/cup/whatever. By all means remove the child, too, if s/he needs to calm down (or if you both do - I've been there a million times over).
In the situation you describe, it would have confiscated the item and would have told DD very firmly that she wasn't to hit anyone. I would also have removed DS from her space and said he wasn't to climb on anyone. If he continued to climb on her, I'd have removed him completely (to another room, the bottom of the stairs - anywhere safe and boring) for three minutes, with an explanation why, and would then have spent those three minutes with DD alone. Repeat until he learns to leave her alone.
If you can sort this aspect of DD's relationships out now, she might be generally less inclined to lash out.
All easier said than done, obviously. And I would love to know from 'old hands' how to deal with a horrendous teenage DD. 