Should/Must I claim my college student children as dependents

I would like to know if I am required to claim my children (both college students) as dependents, or if I should even if not required.

I have run TurboTax on both scenarios.

Because of my income, I will not get any tax credit by claiming their tuition.  My tax due did not change at all by entering their 1098-T's or any other college info... and reading the worksheet confirms that it is because of my income.

Running a second set of tax files for all of us, TurboTax calculated that my Tax due will increase by $1000 if I stop claiming them as dependents (they are 19 and 21 and live at home when not at school).  However, EACH of THEIR tax refunds will change by + $1000 by filing as not being my dependent.   This is a net change of + $1000.00 for the household.

Is it legal to stop claiming them as my dependents?  Is it a good idea?  Is it possible that these calculations are wrong?  Would I be able to change back next year if the numbers warrant it?  thanks for your help.