First transaction fees could be set as low as 1Sat/Byte ... the UXTO on the scond would be from the unconfirmed first Tx, so spending it with high fees is to accelerate and promote its confirmation, and its confirmation will entangle with it the confirmation of the first tx.. as the first is a parent transaction!
But in this way, you would have to pay more fee. It would be better to make a single transaction with high fee.
Take note that miners would prioritize CPFP transactions based on their effective fee rate, not based on the fee rate used for the child.
The effective fee rate is equal to the fee paid for both transactions divided by their total (virtual) size.