The problem with online students is that there is often no way to verify their excuses. The end of a term is a particularly dangerous time to be a grandparent of an online student.
I always follow my late policy unless the student has extenuating circumstances as to why they are late. And I make it clear to the students at the beginning of class that it is up to me to determine whether or not a circumstance is extenuating (but general rule of thumb is that it is something that has happened that is out of the control of the student).
It is very important to explain your late policy to the students at the start of class and be consistent in enforcing it.
I create deadlines that are realistic and then stick to them. For example, any work that is entirely individual (homework, quizzes, etc.) may be submitted at any time during the course. However, work that is collaborative (discussions, teamwork) must be done along with the rest of the class or team. I never extend discussion or teamwork deadlines for an individual student. That would be like letting a student sit in an empty classroom and talk to herself.
