Not Aer Lingus recently but did book through British Airways. I booked car hire in the U.S at a great price. Aer Lingus had it on at the same rate when I later checked. It was through Avis. I have booked car hire at the same destination several times previously but never as cheaply. All worked out well on pickup and return and no extra fees were due.
I have booked car hire while booking an Aer Lingus flight. It was cheap, but I had to make changes to the date later, and that was more complicated (and there were charges) than if I had left the car till later. I didn't quite understand which company I was booking through.
Sorry, wasn't USA though