Not sure how to follow up with this. Normally I love SW but had a terrible experience last week.

Flight: DC to Midway (Chicago) to Portland, OR
Left DC late and landed moments before the connecting flight was scheduled to leave (and was last flight out that day)
Ran to the gate and the door was still open, plane was still there, gate attendants were still there, and they wouldn't let us board because their system had automatically rebooked us for the following morning when mid-flight from DC.
Me: "let me get this right, we paid for tickets on that plane right there, there are still seats open, the doors is open, the plane has not left, and you won't let us on?"
SW: "Yes, we've already sent in our numbers"

Told us we could sleep in airport or book hotel at our own expense.

We pressed once more for hotel after showing the DOT regulations about traveler rights and they handed us a paper with a QR code to "request a Southwest LUV voucher". We asked why she didn't give us that to begin with and she said, "we can only give them if you ask for them." How can we ask for something we don't even know exists?

Booked a hotel and flew home the next day.

While we were direct we never once yelled or caused a scene and even checked in with them to see if they were doing OK given the tense situation. The staff was incredibly dismissive and treated us as though we had done something wrong.

On the flight over I knew the turnaround was going to be squeaky tight so I kept asking the FA how we could figure this out. She repeatedly kept throwing her hands up in the air saying "sir it's all out of my control there is literally nothing I can do for you." Then she sat back down and started doing stuff on her phone again. (bumpy flight so everyone had to stay seated).

All around it was the worst experience flying I've had with SW or any other customer service experience for that matter.

Any advice for how to follow up?