Hypnos

Phoenix. 

Guess I missed the joke.
Some of us are immunocomprimised and must rely on others to do their duty.

Religious waivers are very difficult to get. Being that she has a history of having her vaccines that adds another hurdle. 
Since she had her vaccines tell her to get the titres test done. If it shows she has all the required shots problem solved. 
If you wait and do the waiver state side you will have a much bigger hurdle to climb. Providing proof of her Religion being against vaccines and many many are not it is just a few from those groups that are but their Religion are actually not against vaccines. Do your research before going down this path. It's not easy and refusing to get the shots after a waiver denial will result in AOS denial. 

With very limited exclusions (e.g. children of certain diplomats)*

This entire thread provokes far more questions than it answers. 
 
I largely concur with the thought that many of these issues were, either directly or indirectly, caused or made worse by your actions, or lack of them. 

Very likely not the full story, nor will anybody ever know the full story.
At this point, the realistic options are to either:
1) Leave within the 33 days, or
2) Start over with a  new I-130 + I-485 packet. The existing AP and/or EAD are no longer valid so they will need new ones. Expect scrutiny.

The IO telling the wife to withdraw the i-30 would not have just come up out of the blue...likely she said something to the IO while the husband was out of the interviewing room which gave the IO reason to suspect fraud/admitted it was not a bonafide marriage.  
 
Legally  married and living together doesn't always equate living in marital union...You are likely not getting the full story from your friend.

I say you may want to research in a correct way starting with reading i485 instructions again:
 
https://www.uscis.gov/sites/default/files/files/form/i-485instr.pdf
 
I485 instructions:
Copies. You should submit legible photocopies of documents requested, unless the Instructions specifically state that you must submit an original document. USCIS may request an original document at the time of filing or at any time during processing of an application, petition, or request. If USCIS requests an original document from you, it will be returned to you after USCIS determines it no longer needs your original.

So I became an LPR on 3rd April, 2013. This meant that according to USCIS' filing calculator I became eligible to file an N-400 on 3rd January, 2018 (plus five years minus 90 days). I filed my N-400 online through ELIS at 2:30am, staying up late because I was excited to finally begin this final chapter in my immigration journey.
 
I hit an early roadblock when the receipt NoA for some reason assigned me an N-400 priority date of the previous day, 2nd January. The "application received on" date was correct since it said 3rd January. I posted about it here more than once, and the consensus seemed to be that USCIS would honour the "received" date, not the "priority" date.
 
It took a year of waiting (thanks, Dallas backlog) but I eventually got my naturalisation interview scheduled for 14th January of this year. I dutifully attended, answered all questions and passed all the tests, but was told a decision could not be made. Well the decision was made tonight, and a denial notice popped up in my online USCIS account. The reason? I applied too early. The notice stated that I applied on 2nd January, 2018, and was only eligible to file on 3rd January, 2018. Again, this wasn't mentioned at the interview, and I brought all my emailed ELIS receipts and other documents showing I filed on 3rd January in case they ever brought it up, but they didn't.
 
So it's been a fun night. After a brief period of shouting, loudly, I began to move into attack mode.
 
What I have done so far:
 
1) Emailed the CIS Ombudsman giving them the entire story, receipts with timestamps showing I applied on the correct date, and all that jazz. Unfortunately, I'm pretty sure the Ombudsman is closed right now as part of the partial federal government shutdown, so I'm not really expecting much out of this immediately.
 
2) I'm going to my Congressman's local office tomorrow to give them the story and all the same documents and seeing if they can intercede with USCIS on my behalf.
 
3) Emailed my old lawyer and another lawyer that helped me back in 2013 to see if they can offer suggestions. Not trying to freeload on them; I offered to pay whatever fee they deem reasonable on this, since it's obviously no longer in DIY territory.
 
4) I'll be contacting the two biggest local newspapers, the Dallas Morning News and the Fort Worth Star-Telegram, to see if they're interested in doing a story on this. I figure the more attention I can get on it the more likely I am to get something done.
 
I also have the option of either filing a fresh application, together with its $725 fee and one year wait time, or an N-336 formal appeal of their decision. Fun fact on the N-336: it costs $700 to file, and you will often wait almost as long as it costs to process a new N-400, so they kinda get you coming and going on that one. I'm not ruling anything out yet, but for now I'm hanging my hat on something from 1-4 getting me somewhere on this.
 
So at the end of the day, anyone intending to file for naturalisation on the day they become eligible: DON'T DO IT. Wait a couple of days, then submit. You will avoid all this bull, and can instead deal with some other USCIS bull that will be unrelated to this.
 
Now it's time to write some letters to newspapers and see if I can get anywhere. I will post replies here as to what happens, if anything meaningful does.

The date the annulment was finalised by the court. 

You can send them together, just don't forget the two sets of documents and separate fees for each application. 

Assuming the husband is a US citizen then two I-130s would be required, one for the wife and one for the daughter. 

A NOIR will list why they intend to revoke the petition (i.e. not a bona fide marriage) and the reasons they believe so. You will need to respond to each point and provide documentation as available. Include a cover letter describing what is enclosed in the response.
 
Somebody else's NOIR won't help you...the reasons will be specific to your circumstances and case.

Can it work? Yes. I don't think the CO would necessarily care too much either.
 
But is it practical? Heck no.
First, you need to be fully divorced and free to marry before you can start the process. Divorce is not something that happens in a day. In many states, there is a cooling off period before issuing a divorce and/or a waiting period after a divorce before you can remarry. You do NOT want to screw either of those up as the new marriage would be deemed invalid for immigration purposes and you would need to start all over.
 
I can't imagine anybody advising to actually do this.

You can also select multiple categories. 

I'm sorry what?
This is extremely absurd. Just stick with the spouse Visa and you wont have to deal with 12 months of AOS process after K1 Visa. Not to mention if I was a consular officer and see in my file that this couple was married, then divorced and immediately applied for K1 so they can get married again - I'd throw it into the "scam" folder. 

https://dps.mn.gov/divisions/dvs/forms-documents/Documents/NewResident.pdf
Yup, you have 60 days of using an out of state license before needing an in-state license.

They need to select an option from this: https://www.uscis.gov/forms/expedite-criteria
Edit: Humanitarian sounds like the closest match to me.

I mean, you made a concious, adult decision to do K1 visa and AOS process. You knew that you wont be allowed to work for a while. This is just a consequence of your choice. 

This entire thread provokes far more questions than it answers. 
 
I largely concur with the thought that many of these issues were, either directly or indirectly, caused or made worse by your actions, or lack of them. 

This entire thread provokes far more questions than it answers. 
 
I largely concur with the thought that many of these issues were, either directly or indirectly, caused or made worse by your actions, or lack of them. 

This entire thread provokes far more questions than it answers. 
 
I largely concur with the thought that many of these issues were, either directly or indirectly, caused or made worse by your actions, or lack of them. 

The letters from your mother in law or letters or intent are completely useless. 
 
Your wife probably needs to go back to the US and establish residency there. Find a job, bank accounts, etc. 

I think they are telling you that someone who has been a resident of Morocco for five years is not a "temporary resident," and that she needs to return to the US to establish domicile.  It is more than just having mom's address and a letter from mom.

1. If she had h1b Visa, why did she need EAD? What was the "big" mistake? 
2. You absolutely made situation worse by pretty much ignoring the whole thing. Who does that? 
3. Did you get a green card through your employer? Was your wife ever offered a green card?  Was she in some process? 
4. H1b Visa only allowes a person a max of 6 years of stay - if your wife was never offered a green card, she would need to leave anyway? 
 
Sorry if this sound harsh but looks like you're in all those troubles mostly by your own negligence.