Whether a bag must be valet-checked is a matter between DL and the passenger. If DL lets the passenger carry the two bags on, he can find space for them. If an FA wants to require that his second bag, the personal item, go under the seat in front of him, that is between the FA and the passenger.

It's basically tough luck. DL permits more carry-ons than there is space and does not do enough about it on small aircraft. Most AA regional carriers prohibit anything with wheels, no matter what size. It's all gate-checked. DL chooses not to do so.

But, you have chosen DL, so you play be its rules.