That's my reading too (and is what the Instructions seem to indicate), but itonewbie pointed out that it could be interpreted as the "joint" credit ($2400 and $1200) is split 50/50 and the child's credit is separate.

But I am just DREADING that if the entire thing is split 50/50, that we will need to determine if MFS is better.  For parents who receive the full advance credits/stimulus, filing separately will result in an extra $550 per child for the credit (total of $1100 credit for the child, split 50/50).