Paperwork needs to prove you are the spouse or parent of a USC. So marriage license or birth certificates.
They can fly on expired passports so long as they expired after January 1, 2020. Do NOT apply for an ESTA for them.
Remember, the ESTAS are ALL automatically cancelled with the current travel ban. So you are both lying and not gaining anything by applying for ESTAS.
Let’s say you pretend they aren’t American and apply for an ESTA. You arrive at the airport and the ESTAS are cancelled. How do you then plan to prove they are exempt from the travel ban? By saying they are American, which starts it all back from the top again.
The embassy is stacked due to being shut for so long. They release regular appointments on Thursday between noon and 2pm and they are usually gone in under a minute. There is an entire (full capacity) WhatsApp group that posts when slots open. It’s genuinely a 3 ring circus.
BUT everyone who has used emergency travel within 5 days has received their passports. Just follow the emergency travel bits on the website and you’ll get it. You’ll have grey hair, but….