If I had a qualifying child from 2019 turn 17 in 2020 as well as having a newborn in 2020, can I qualify for the additional $1100 of Covid Relief money for the newborn ?

The child must be under 17 years old to qualfiy for the recovery rebate credit. A dependent over 17 years old doesn't qualify for the recovery credit but other dependent credit for $500 on your income tax return, if qualfiied.

Did you get a Stimulus payment for them before?  Yes it washes out with the baby.  

The Recovery rebate credit is really based on your 2020 return.

In your case, you received a stimulus for 1 qualified dependent based on your 2019 return.  Now that you are filing your 2020 return, your child is no longer under age 17, so he does not qualify and you only have 1 dependent that qualifies (the baby).  You received the stimulus already for 1 dependent.  

Sorry, the credit is based on the number of qualifying dependents you claim, not their identity.