milimelo

This is a pretty ordinary denial. You described it well in your own words. There's no way she can visit the US until she gets an immigrant visa.

Okay, here’s my report. Nobody demanded a return ticket. Everything went smooth. Thanks everybody!

If check wasn't cashed, put a stop on it and then send in a new packet. 

To answer your question: 
You can definitely remarry your wife. But, you might not be able to successfully sponsor her for a green card. It doesn’t matter if you wait another 2 years or get married now. 
Your timeline and turn around is fairly tight. 
First daughter was born in 2012 (wife was 23 you were 27)
****2 more children AND a divorce AND a move to the US in 3 years…*****
Second marriage occurred: 2015/2016
ROC: 2017/2018
Apply for and obtain Citizenship: 2018-???
Decide to divorce: 2021/2022
Second Divorce Finalized: 2022
 
I suppose it depends on how long after you received citizenship you stayed together… but if the marriage was falling apart in 2020 due to COVID. Upon reflection it might seem like you separated immediately after you received US citizenship. 
Delaying your reunion/remarriage with your first wife might not also seem “natural/believable” because you’ve clearly been in communication with her as you have three children together and appear to coparent successfully as your first child is encouraging you to reunite with your first spouse. 

Even one with a "prestigious job"?  
 
Jeez.
 
Honestly, sounds like you're looking for a babysitter for your kids.  Good luck, I'm out.

I would not rekindle a relationship with someone who isn’t interested in moving to the US. In addition, if she was an addict you might require a waiver for her depending on what type of addiction she had. Especially if her addiction is the reason you decided to separate. USCIS might assume this was all a long term plan: divorce, obtain US citizenship and then bring your entire family to the US so you can all become US citizens and reunite. 
USCIS might want you to supply your wife’s entire mental health history and her journey to a better state. If she is not even interested in moving to the US why go through such a big ordeal. Maybe just sponsor your children and obtain their US citizenship. Then date your wife long distance.  You’ve only been single for 2 years, no need to rush things. 

Maybe it's a cultural thing, but this is a very strange situation.
 
Doubtful she would get a B visa though.

You can run into serious issues if she doesn't file the I-751, Petition to Remove Conditions on Residence. 
 
Why did you never do this? Are you unaware of the USCIS procedures? This may look irresponsible in the eyes of the USCIS. Hopefully it doesn't jeopardize too much. 

You're worrying unnecessarily. One way on K-1 is normal and expected.

If check wasn't cashed, put a stop on it and then send in a new packet. 

I think the smartest and safest option it’s go together to the interview. 

One can argue you're applying based on marriage to US citizen and the spouse should be allowed in because of that. In rare cases they get asked a few questions, even informally.

You're worrying unnecessarily. One way on K-1 is normal and expected.

You're worrying unnecessarily. One way on K-1 is normal and expected.

If check wasn't cashed, put a stop on it and then send in a new packet. 

If check wasn't cashed, put a stop on it and then send in a new packet. 

Additionally, you need to have had certain amount of time with the child in your custody - check the links provided earlier - 2 years is what I've seen mentioned. 

It does not require it per say. You can apply for daughter's US passport first.
 
But it is a crucial piece of evidence. If I was you, I'd spend 1100 to get the certificate in the next year or two. The reason for that is simple. Sometime in the future, many years later, when renewing passport, your daughter may be asked for some additional proof of US citizenship. If you or your spouse are no longer around (we're all mortals unfortunately), your daughter may have difficulty gathering all your papers and documents to prove her citizebship.
 
Additionally, this question about citizenship may come up if your daughter ever decides to sponsor a foreign spouse for Green Card.
 
Those are just two common cases when this may come up. But I'm sure this can also come up if she decides to take up jobs in the US military / government / other agencies.
 
The best thing is to spend the money, get the cetificate, make copies for yourself (cannot make copies and distribute, it's a crime) and store it in a safe place.

I 601a would not be applicable in this case, if needed it would be a I 601.
 
The I 130 has not been denied.

No. 

That is not enough. 
 
 
@madmanmike,
 
Page 8 of the I864 instructions state:
"If you were not required to file a Federal income tax return under U.S. tax law because your income was too low, attach a typed or printed explanation. If you were not required to file a Federal income tax return under U.S. tax law for any other reason, attach a typed or printed explanation including evidence of the exemption and how you are subject to it. Residence outside of the United States does not exempt U.S. citizens or lawful 
permanent residents from filing a U.S. Federal income tax return. See Filing Requirements in the IRS Form 1040 Filing Instructions to determine whether you were required to file."
 
You must attach a full explanation in letter format to your I864 package. 
 
I strongly suggest reading through the I864 instructions until you have full understanding of what is expected. It's very likely seeing that I864 RFEs are generic, that you have more discrepancies than you think. 

No. Each files a standalone I-130 so in case grandmother dies, there's the other I-130 to fall back on. 

I am not sure you are actually helping your friend, much better if your friend joins.
 
You said well implied that the child had attended school in the US, how? Did the child have a Student Visa.
 
There are some things you have mentioned, intimated, that might cause problems but without the full story I am loathe to say anything else.
 
The Mother can certainly delay things until the daughters case catches up.
 
I think as a general comment it is better to file a new I 130 that wait for the I 824.

Tourist visa is for visiting only.  If she enters on that and attempts to stay (‘normalize her status’), that’s immigration fraud. Potential lifetime ban from the US and surely not worth the risk? 
 
But you’ve been told this repeatedly throughout the thread and are still not listening, so I’m out. I wish them the best of luck, but would strongly suggest you let them know the potential risk they’re taking if they decide not to simply delay Mom’s interview and go through the proper legal route. 

The link is clearly from Adoption part of USCIS - so wouldn't have been applicable to your child. All you had to do was complete the DS-11 form (and gotten his birth father to complete the form as he was absent but consent(ed) to US passport issuance, get it notarized), booked an appointment with either local post office or special issuance agency if you had to return urgently after arrival to the US and gotten the child US passport. 
Green card only comes if you've actively done your part which is paying the USCIS green card issuance fee - not required for minor children who will become citizens after entering the US with immigrant visa.