I second what @lifesabeach85 said - DH went home briefly both times to shower and change (and say hi to DD1 the second time). I think he maybe brought a change of clothes and toothbrush/toothpaste and a pillow.
Unless I get induced I don't foresee being able to pack our own pillows--even our Kindle/ipad stuff we use every day at home, so I'm not sure what the odds are that we'd actually get to pack them. I might pack them in the car on the days that I have doctors appointments just in case.
I think the majority of people will have plenty of time to put the things they need in their bag/car before they have to head off to the hospital. I haven't heard of that many people IRL who have to rush straight from an appointment to the hospital, so I really wouldn't worry too much about not being able to pack everything you need. There's a very good chance you'll have plenty of time to pack it!
Re: Hospital Bag Essentials
DD1: 8/2014
TTC #2: 6/2017
BFP 8/3/2017 | CP 8/4
BFP 10/16/2017 | CP 10/21
BFP 12/18/2017 | CP 12/28
BFP 2/15/2018 | EDD: November 2nd | It's a girl!
DD2: 10/2018