It's not his mom. It's his step mom.
But I agree with you. Human are not trash. And I don't know why the boy couldn't move either
The dad was probably the one who wanted to throw the child away and probably threatened the step-mom to throw her own kid away. He wasn't drugged I believe, but there was no indication he was drugged they said he just didn't wake up and thought the child was broken. He woken up when he heard yelling but he probably has problems with his legs because he couldn't seem to stand nor walk properly so that could also be a reason why he wanted to throw away the child. The author probably didn't want to cause too much drama and just did a quick fixer upper, but the dad is still an ass, but apparently he's fixing his behavior.
I reread this after so long and i still couldn't understand oujirou's dad and his wife at all. Like how the hell did they come into decision to throw away a human being? Why was the wife okay with it? Why did the kid suddenly wake up? Was he drugged before or what? Why did the dad suddenly come into his senses after years of being a piece of shit? Confusion. Good manga tho.