You do not qualify as their dependent children because one of the qualifying requirements is that, if the child is married and files a joint return with their spouse for any reason other than getting a refund of tax withheld, then that child does not qualify as a dependent. Since you would claim education credits, you are filing for a reason other than a refund of tax withheld, so you are not a qualifying child for them.
Your parents cannot decline to claim you under these circumstance. . It is YOUR choice whether you want to file jointly and claim yourselves and your education credits because you are then not qualifying children for them.
One of the questions to qualify you as their qualifying child dependents asks if you were married, then if you are filing a joint return only to receive a refund. If you are filing for the refund of tax paid, plus any other reasons, yo cannot be their qualifying child dependent. Since you don't qualify for them, you claim your own exemptions by filing jointly and NOT checking the box that says you can be claimed by someone else.
See the following from page 15 of IRS Publication 501:
"Joint Return Test (To Be a
Qualifying Child)
To meet this test, the child can't file a joint return
for the year.
Exception. An exception to the joint return test
applies if your child and his or her spouse file a
joint return only to claim a refund of income tax
withheld or estimated tax paid.
Example 1—child files joint return. You
supported your 18-year-old daughter, and she
lived with you all year while her husband was in
the Armed Forces. He earned $25,000 for the
year. The couple files a joint return. Because
your daughter and her husband file a joint return,
she isn't your qualifying child.
Example 2—child files joint return only
as claim for refund of withheld tax. Your
18-year-old son and his 17-year-old wife had
$800 of wages from part-time jobs and no other
income. They lived with you all year. Neither is
required to file a tax return. They don't have a
child. Taxes were taken out of their pay so they
file a joint return only to get a refund of the withheld
taxes. The exception to the joint return test
applies, so your son may be your qualifying
child if all the other tests are met.
Example 3—child files joint return to
claim American opportunity credit. The
facts are the same as in Example 2 except no
taxes were taken out of your son's pay or his
wife's pay. However, they file a joint return to
claim an American opportunity credit of $124
and get a refund of that amount. Because
claiming the American opportunity credit is their
reason for filing the return, they aren't filing it
only to get a refund of income tax withheld or
estimated tax paid. The exception to the joint
return test doesn't apply, so your son isn't your
qualifying child.
<a rel="nofollow" target="_blank" href="
https://www.irs.gov/pub/irs-pdf/p501.pdf">https://www.irs.gov/pub/irs-pdf/p501.pdf</a>
Note in the publication under Qualifying Relative tests, the examples include one showing that this test holds true. If you file a return for anything other than just a refund of tax, you do not qualify your parents for the Qualifying relative dependency either.
Example 2—return filed to claim refund.
The facts are the same as in Example 1 except
your friend had wages of $1,500 during the year
and had income tax withheld from her wages.
She files a return only to get a refund of the income
tax withheld and doesn't claim the earned
income credit or any other tax credits or deductions.
Both your friend and her child are your
qualifying relatives if the support test is met.
