Just some additional trivia since I see it as a very interesting subject.
父は、車に乗って飛行場に行った母を追いかけた。 Dad went after mom who took the car to the airport.
父は車に乗って、飛行場に行った母を追いかけた。 Dad went after mom taking the car to the airport.
As mentioned, there are no strict rules on where you cannot put a comma in Japanese, but there are cases that when if you don't put in in a certain place, it changes the whole meaning of the sentence. Of course, this can be avoided altogether by restructuring the sentence.
車で飛行場へ行った母を父は追いかけた。Dad went after mom who took the car to the airport.
父は車で母を飛行場まで追いかけた。Dad went after mom taking the car to the airport.
If you search "読点で意味が変わる" in Google, there will be a bunch of articles on it so it's an issue with even the Japanese people.