Yes, the check goes to whoever the child lives with. If she's named as payee, the child must live with her. That does not mean that the child doesn't get a check, just that SHE is not getting it or named on it. Once the child comes to live with you, then you notify social security to change the payee information and address on the check, and they'll send you the same paperwokr telling you to inform them any time the kid leaves you to live with a different guardian, becasue YOU will no longer be entitled to the check.

The extra she gets for child support from another parent is not calculated in as income to her for the purposes of calculating child support, but might be counted as "other resources" to her for the purposes of deciding how much (if any) alimony she deserves to get. It's not "income". It's an outstanding debt owed to her by someone else and she is lucky enough to have the government helping to pursue the deadbeat dad and arrange assignment of wages & such, as opposed to the rest of us in the world who are owed money by some deadbeat (not child support money, but something else), and have to go through the process of suing them & figuring out all the details of how to collect it from them if we win our lawsuit. It's JUST a debt owed, and if there is a set payment of it that's pretty guaranteed, then it's an "other resource".