By 0800, 1st, 2nd(-), 9th and 12th Corps had orders committing them to the attack. McClellan only held back the two divisions in the centre (Sykes and Richardson).
A large part of the problem was that early evening on the 16th, Sumner returned to his tent at Keedysville. The 1750 order from McClellan was for Sumner to get the 12th Corps to Hooker immediately. This led to the 12th Corps, newly arrived on the field, getting lost because Sumner, the officer charged with getting them to where the army commander directed them, went back to his tent to sleep. Worse, the next morning Sumner went to the wrong place (Hooker's old HQ) and say there for an hour whilst McClellan's staff were searching everywhere for him. Fortunately, they'd started Sedgwick and French without him.
Sumner, at the head of Sedgwick's division, doesn't reach the area where 5 divisions under his nominal command have been fighting. Arriving at the East Woods ca. 0830-0900 he is met by Meade (by McClellan's order now commanding 1st Corps), a staff officer from 12th Corps (reporting Mansfield was dead and Williams in command), and a staff officer from McClellan with the orders:
"Gen. Hooker appears to be driving the enemy rapidly. If he does not require your assistance on his right, please push up on his left through the ravine at the head of which the house was burned this morning, getting possession of the woods to the right as soon as possible & push on towards Sharpsburg and a little to its rear as rapidly as possible. Use your artillery freely."
McClellan's orders told Sumner's 2nd Corps (distinguishing his roles) to do one of two things depending on the situation. He was either to form on the 1st and 12th Corps' right and push into the West Wood's if the 1st and 12th Corps lacked the combat power to do it, OR he was to form on their left and attack the Sunken Road position and the Dunker Church. He did the latter, forming his three available divisions (including a division of 12th Corps) in a line and advancing 3 divisions abreast in a SW direction.
Sadly, Sumner played division commander on his right flank, rather than hanging back to keep command of his wing. At 0910 McClellan, who'd seen McLaws moving to attack Sedgwick, sent a warning to Sumner. However, Sumner wasn't anywhere near the signals station, and it never got to him. No-one was available to react to the warning.
Essentially, I think Sumner thought he was entering a pursuit phase, whereas the enemy was just committing their reserves to counterattack.