On my personal info (and my wife's) we've noted we live in a foreign location. I've noted that each of our children lived outside of the US for all 12 months of 2020. Is it okay to use my parent's address for our mailing address?
Yes. You can use your parent’s address as your mailing address. The IRS just needs a mailing address in case they have to send you something in the mail—or if you asked for a refund check instead of direct deposit.
The only issue you may have is if both your and/or your parents claim the Earned Income Tax Credit or Advanced Child Tax Credit. The IRS looks for instances where more than one household using the same address claims these credits as some families will split their households to illegally claim double credits.
Remind you parents to notify you promptly if you receive any mail from the IRS. Audit notices come with a clock and need to be addressed promptly.
The IRS might need the address only to contact you, BUT some states are aggressively looking for additional revenue. Be aware that some states are now going over federal returns looking for people with mailing addresses in their state who didn't file as a resident. With no other supporting data they are then sending out demand letters saying "we think you are a resident so refile your taxes and pay us $X plus interest and fees." I would highly avoid using any mailing address that isn't in the same state or country as your residence.