If you equip a shield you lose the 2nd attack, effectively giving you half the damage you have without a shield.
That's completely wrong. I know because I specifically tested it on request. With a shield equipped, you do one attack. Without a shield equipped, you still do one attack, but the damage/absorption is displayed as being split into two attacks, but the total damage dealt and absorbed is the same, shield or not.
(And as I said five posts up, when I actually zoomed in to watch the attack, I saw that the left hand shoves, and the right hand was the one which attacked twice with the dagger.)