The rules for the $1,400 rebates are set forth starting on Page 342 of the American Rescue Plan Act, which can be found at

https://rules.house.gov/sites/democrats.rules.house.gov/files/BILLS-117HR1319EAS.pdf 

What you might find interesting is this attempt to allow IRS to figure out a way that the same kid doesn’t get counted twice, when claimed as a dependent (or exemption) in alternate years:

‘‘(h) REGULATIONS.—The Secretary shall prescribe such regulations or other guidance as may be necessary or appropriate to carry out the purposes of this section, including—
‘‘(1) regulations or other guidance providing taxpayers the opportunity to provide the Secretary information sufficient to allow the Secretary to make payments to such taxpayers under subsection (g) (including the determination of the amount of such payment) if such information is not otherwise available to the Secretary, and
‘‘(2) regulations or other guidance to ensure to the maximum extent administratively practicable that, in determining the amount of any credit under subsection (a) and any credit or refund under subsection (g), an individual is not taken into account more than once, including by different taxpayers and including by reason of a change in joint return status or dependent status between the taxable year for which an advance refund amount is determined and the taxable year for which a credit under subsection (a) is determined.