Ok, I know trolls didn't fight at Erebor in the book; Jackson decided to include them in the film.
Shouldn't they have turned to stone during the day?
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Because not all Trolls turn to stone in daylight.
Last of all Húrin stood alone. Then he cast aside his shield, and wielded an axe two-handed; and it is sung that the axe smoked in the black blood of the troll-guard of Gothmog until it withered, and each time that he slew Húrin cried: 'Aurë entuluva! Day shall come again!' Seventy times he uttered that cry; but they took him at last alive, by the command of Morgoth, for the Orcs grappled him with their hands, which clung to him still though he hewed off their arms; and ever their numbers were renewed, until at last he fell buried beneath them. Then Gothmog bound him and dragged him to Angband with mockery.
Thus ended Nirnaeth Arnoediad, as the sun went down beyond the sea.
Trolls not turning to stone is not a novel invention either; the above passage is from the Silmarillion giving an account of a disasterous (to Elves and Men) battle from the First Age which included Trolls, and which took place in daylight.
This is made explicit by Letter 153:
But there are other sorts of Trolls beside these rather ridiculous, if brutal, Stone-trolls, for which other origins are suggested.
It's therefore wrong to assume that just because it's a Troll it should turn to stone in daylight. There are different subspecies of Trolls, of which Stone-trolls are the only one that turns to stone.