longwaytogo I feel for you
my dd is 4.5y and my ds 19m and not too long ago we had a very bad phase of 'I want what he/she has'... equally bad from both sides... ds is a relatively well tempered little sole, but when he wants something he WANTS it. As he's heavier than his sister it's sometimes quite funny to watch them wrangling. DS just sits on her if he's had enough.
How we dealt/deal with the constant winging/fighting etc.
At first I got really upset and intervene left right & centre which was driving me absolutely bonkers as I couldn't get anything done without being disturbed by one or both of them crying/winging etc. and it didn't really make any difference. DD is old enough to understand explanations and punishment, but ds isn't quite old enough.
Next approach was to have 'spares' at the ready, i.e. distraction tactics. If dd had a water squirter I dug one out for ds etc. But then of course we go the 'he's got the blue one, I want the blue one!' Which was o.k. because ds doesn't care what colour as long as he can chew on it.
Next step was ignoring bad behaviour (but making sure obviously e.g. dd wasn't using ds as a trampoline) and encouraging good behaviour, i.e. nicely playing with each other - shamelessly using sweeties, TV etc. as bribes.
We thought we had a breakthrough when ds was ill with chickenpox... I told dd to let him play with xyz as he's poorly. And would you believe it? She did.
And just recently we've done a 180 deg turn and it's gone all downhill again. Only 2 days ago dd slammed ds against a door head first and yesterday ds wacked dd as she kept toppling him over... and he's got a good left hook!
So you see, you are not alone. Not very comforting I know but maybe it helps you to come to grips with your lo's being in the 'destructive/violent' phase.
One thing I do if I can't take it anymore is I just leave the room for a lot of deep breathing (only of course if I know they haven't got anything within reach to seriously injure each other). DH simply grabs a can of beer 