If a relative filed my child for the 2019 tax year, will they get the $500 child credit for the stimulus or can I add my child to my stimulus credit?

[Hal_Al]

They will get it.  There is no way to "add your  child to your stimulus rebate"

If you haven't filed 2019 yet, and you claimed your child on your 2018 return, there's a chance you both may get the $500. 

Why did a relative claim your child? That is allowed under certain circumstances. 

.A child closely related to a taxpayer can be a “Qualifying Child (QC)” dependent, regardless of the child's income, if:

1. He is under age 19, or under 24 if a full time student for at least 5 months of the year, or  is totally & permanently disabled
2. He did not provide more than 1/2 his own support
3. He lived with the relative (including temporary absences) for more than half the year. That doesn't mean you lived in the relative's home. It just means you lived in the same home. 
4. He is younger than the relative (not applicable for a disabled child)
5. If the child meets the rules to be a qualifying child of more than one person, you must be the person entitled to claim the child as a qualifying child (this essentially means that you have the parent’s permission to claim the child, if the child also lived with the parent more than half the year)
6. If the parents of a child can claim the child as a qualifying child but no parent so claims the child, no one else can claim the child as a qualifying child unless that person's adjusted gross income (AGI) is higher than the highest AGI of any of the child's parents who can claim the child.

https://turbotax.intuit.com/tax-tools/tax-tips/Family/Rules-for-Claiming-a-Dependent-on-Your-Tax-Ret...

[Mlynne]

I have claimed both of my children for the past three years. They are both young and under 17. They were both on my tax returns and were qualifying.

I only received one 1200 payment and 500 for one child. I do not understand why I did not receive the other 500 payment for my second child. He is qualifying and lived me every year. I have claimed him every year.

Why is this happening?

@Hal_Al 

[VictoriaD75]

The IRS has said they would base stimulus payments on 2019 filings. If you have not filed for 2019, they may have deferred to your 2018 return. If you feel you did not receive the proper amount for your stimulus payment, only the IRS will be able to resolve the issue. This will also be reconciled on your 2020 tax return. You may have to wait until you file your 2020 return to get the additional stimulus for your dependent. The qualifications for the stimulus payments can be found in the links below. 

What do I need to know about the coronavirus stimulus package?

Economic Impact Payments