Let’s look at an example
D’s taxable scholarship (r&b) $15,000
S’s taxable scholarship (stipend, travel, etc,) $20,000
unearned income subject to kiddie tax: D $8,700 ($15,000-$6,300 std ded)
S $13,700 ($20,000 -$6,300)
Parent taxable income (AGI minus item ded or std ded, minus personal exemptions) $30,000
Total of D and S unearned income: $22,400
Parent tax on $30,000 from tax table MFJ $3,576
Parent tax on $52,400 from tax table MFJ $6,936
Difference in parent tax $3,360 (total kiddie tax)
D’s part of kiddie tax $8,700/$22,400= 0.39 $3,3600.39=$1,310
S’s part of kiddie tax $13,700/$22,400=0.61 $3,3600.61=$2,050
They both pay a 15% tax rate D $1,310/$8,700=0.15
S $2,050/$13,700=0.15
If D had been the only one in this example to have income subject to kiddie tax, then her tax rate would still be 15%.
$30,000 parent taxable income plus $8,700 = $38,700
parent tax on $30,000 $3,576
parent tax on $38,700 $4,881
difference $1,305
$1,305/$8,700= 0.15
Also if D has $5,000 in income from working, that would bring her unearned income subject to kiddie tax up, because the standard deduction of $6,300 would cover less of her taxable scholarship income.
So if D had income subject to kiddie tax of $13,700 ($20,000-$6,300)
then together with brother the total income subject to kiddie tax would be $27,400
added to parent taxable income $30,000+$27,400=$57,400
parent tax on $30,000 $3,576
parent tax on $57,400 $7,686
difference $4,110
D’s kiddie tax $2,055 tax rate $2,055/$13,700=0.15
S’s kiddie tax $2,055 tax rate $2,055/$13,700=0.15
So in all of these scenarios where parent tax rate seems to be 15% and stays 15% even with adding $8,700, $22,400 or $27,400 of unearned income subject to kiddie tax, the tax rate also stays the same for each child.
Of course that might be the case in your situation, or not. Also once D files taxes independently she could possibly pay less in tax (10% bracket), but then the parent would lose one personal exemption, which might or might not change their tax rate, or parent income could go up, lots of variables.
But the bottom line is, that you are still better off having a $15,000 taxable scholarship.