I'm going to stay at the table even though my father coughed really hard across the entire table.
Why wouldn't you leave?
I'm not going to leave the table because I'm enjoying my dinner.
While you shouldn't have to leave the table, it is unacceptable for someone to cough onto a table during a dinner. You may be enjoying your meal, but making a statement would let them know how rude it is to do something like that while everyone is trying to enjoy a meal.
I doubt it was intentional.
Only you would be able to determine that. Did your dad try to cover his mouth?