milimelo

AOS is at least a year or two down the road as it looks like she hasn't even started I-130. Worry about that at NVC time - she can depart early and get a job in the US, get a joint sponsor...

You currently have a household of three which will be increasing to household of 5 with your spouse and stepdaughter's arrival. 

You currently have a household of three which will be increasing to household of 5 with your spouse and stepdaughter's arrival. 

You go online on uscis.gov and pay the green card issuance fee. Need the info off the issued immigrant visa to pay it. 
 
For SS number, if he checked off on Ds-260 to have it issued, wait two weeks post arrival for it to arrive and if not there, complete the form on SSA.gov and go in to a local SSA office. 

AOS is at least a year or two down the road as it looks like she hasn't even started I-130. Worry about that at NVC time - she can depart early and get a job in the US, get a joint sponsor...

Cash must always remain an option - legal tender is legal tender. I hope the lawsuit makes it clear that an entity can't just decide they're not accepting US legal tender. Couldn't care less if it takes them more time to account for cash, not my problem. 

Cash must always remain an option - legal tender is legal tender. I hope the lawsuit makes it clear that an entity can't just decide they're not accepting US legal tender. Couldn't care less if it takes them more time to account for cash, not my problem. 

I've seen medical requests reported here for UK folks when applying for B1/2 visas and a history of alcohol-related incidents - fights and similar. 

Cash must always remain an option - legal tender is legal tender. I hope the lawsuit makes it clear that an entity can't just decide they're not accepting US legal tender. Couldn't care less if it takes them more time to account for cash, not my problem. 

Cash must always remain an option - legal tender is legal tender. I hope the lawsuit makes it clear that an entity can't just decide they're not accepting US legal tender. Couldn't care less if it takes them more time to account for cash, not my problem. 

Cash must always remain an option - legal tender is legal tender. I hope the lawsuit makes it clear that an entity can't just decide they're not accepting US legal tender. Couldn't care less if it takes them more time to account for cash, not my problem. 

It seems they very much suspect immigrant intent, being married to a USC was already a strong tie to the US. Her travel history of being turned away for things like no return ticket and heavy baggage and then being denied again after getting a B....odds do not look good. It's only been 1 year since she denied entry.
 
If it were me, applying for another B doesn't seem worth it. Better just go straight to the immigrant visa application and plan to live in the US for a bit. I think the only way she can overcome immigrant intent is applying for the spousal visa, then either live in the US for a bit and relinquish the green card or just relinquish the GC right after entering on the spousal visa. Frustrating but I'm just not seeing another way around this.

3 years (can file 90 days prior) of having been an LPR (from the date the first green card was issued), and being married for 3 years to a USC. From little you listed, she could've applied even before her 10-yr green card was approved. 
Strongly advise applying before new fee increases go into effect in April. There's online filing option now for N-400. 

Upon entry into the US with a valid immigrant visa, your passport will be stamped by CBP to endorse the visa.  At that point, you are a legal resident.  Your endorsed visa becomes a temporary Green card until the plastic one arrives (or up to a year from date of entry).  You can IMMEDIATELY exit and re-enter the US later using your stamped passport.

1. Will her job continue once she moves back to the US, if so evidence from her Employer, otherwise a Joint Sponsor. Expedite, what? On what basis.
 
2. I do not what she has, but she might want to update her DL, Bank Account, Credit Cards etc on her next trip home. Sometimes it is best for the USC to move first. I suppose how long the job process would take will depend on what she does, process takes about 18 months so quite a bit of time in a changing employment market.

If he has orders and you're listed on them, push for 319b naturalization. 

If you're on his orders, look into expedited naturalization. 

If you're on his orders, look into expedited naturalization. 

Your daughter and you need to figure out your priorities: GC and live in the US or school in England this Fall. 
The issue with adjustment is that there is no set time table and as you’ve seen no rhyme or reason to when a GC will be issued. 
I would do as @Verrou suggests delay going to school this Fall and start in the next semester or next year. this will give you some breathing room in case the GC does not arrive in time. then once your daughter has her GC she can file the I131 so she can leave the US for up to 2 years without abandoning her GC. 
Unfortunately the only way to “save” this adjustment application is if she already has advanced parole and is allowed to leave. if she does not have AP her AOS will be deemed abandoned… and you’ll have to figure out next steps if she receives a denial notice.
 

Biggest issue is just getting there. Probably should designate Almaty, Kazakhstan or Tashkent, Uzbekistan as the processing post. Warsaw, Poland is the currently designated as the processing post for Russian citizens but Poland basically bans Russians from entry, though that could be worked around by flying to any other Schengen Zone country (e.g. Germany) and crossing over the border into Poland (internal borders for Schengen are unstaffed and don't perform any kind of inspection).
 
Alternatively you could probably just put Moscow, Russia as the post and deal with it once the time for an interview comes. What you put on the I-130 is more of gentle suggestion than a strict requirement on the state department, they will schedule it wherever they see fit and if that doesn't work for you for any reason you have to argue with the state department to move it elsewhere. Only thing that designating the post on the form does is tell USCIS "this person is abroad, forward this I-130 to the national visa center on approval" with the alternate option being "this person is in US, hold onto it for AOS".

The petition I filed back in 2010 was approved in 2012 I believe (F4) - NVC has yet to contact me or the beneficiary to get started with anything. I do however save my yearly tax return transcripts just in case. 

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.