Jamila ak

refer to USCIS i-130 page for details on where to file, appears only three lockboxes accept the i-130.
 
I second Arden's advise though, file on-line.

The best is to file online.

That is not a list of required evidence.  That list follows the words "In addition to the required...."  The couple lives together in Lebanon.  Evidence of that is enough.  They have children together.  Even that is extra.

Agree they seem to have a few issues but legit relationship does not seem one of them.

Thanks guys and gals for your feedback, it was very helpful, we are gathering the package for the I-130 and will keep updating, should I start a timeline when package gets sent out? 
 

OP has mentioned she lives in Lebanon now quite how you persuade the Consulate you will go back I have no idea.

It doesn't matter, the odds of OP getting a tourist visa are low. The arrest warrant clearly doesn't help but in general having a USC spouse will make it very difficult. Even when the USC spouse lives abroad and has been living abroad for years, it's common to get the 214(b) denial, it happened to us when my husband applied despite that I had a years long work visa and had been living abroad for years. There's often a strong suspicion that the spouse will use the tourist visa to enter and adjust status and it's hard to overcome, even when the USC lives abroad. It's probably harder in some countries than others, given overstay patterns by nationality.
 
I've seen threads here on VJ where a foreigner + USC spouse both living abroad had to attempt like 4 or 5 times before finally getting a B approved. Or the even more extreme route: file the I-130, get the GC and then relinquish the GC to prove you have no interest in living in the US, then maybe they will see you have no immigrant intent to approve the B.

**Three derailing posts removed. Please stick to the topic of helping OP figure out what they need.**
 
VJ Moderation

Domicile is not the requirement, “intent to establish domicile” is what is needed and that is fairly easy to demonstrate.
The question of whether an I130 can be filed - the answer yes is correct.  The support affidavit is a hurdle but it appears you folks have overcome that.
 
Good luck to both of you, hope this works out

I think it might be a good time to retire the argument that kids "only prove people had sex". If that was the case, birth certificates of children would not be listed in immigration forms as acceptable evidence of relationship. 
 
So, yes, OP, you can and should obviously present the birth certificates, but one kind of evidence alone is hardly ever enough. Try to gather as many documents as you can that show you share a life together on social and financial aspects: joint health insurance, leases or mortgages, joint bank accounts, wills, utility bills, etc. If you don't have some of those it is not the end of the world, but don't rely on your kids' birth certificates alone if you want your case to be solid.

All you need to file a petition is proof of US citizenship, proof of marriage, proof of bonafide relationship (birth certificates of your children and proof of cohabitation in Lebanon should suffice). You will fill out the  I-130 and I-130a and pay the fee. You can do this online or send your documents to a lockbox. 
Domicile is only looked at during the NVC stage. 
Has the US citizen spouse filed US taxes the past 7 years? 

There is no reason for him to delay filing the petition.  Domicile is not an issue at petition stage.  It comes up at the same time as the financial sponsorship issue does, AFTER the petition is approved.

Well I will overlook the issues others have raised. Like if you want to ask regarding purely theoretical scenarios go ahead but be clean about it.
 
Yes, as long as he's in prison for something other than a sexual offense against a minor under the Adam Walsh Act or if he was ever convicted for such offense previously. AWA determination can be overcome, but he'll basically have to prove "beyond a reasonable doubt" (i.e. 99% confidence) that he is not a threat to you or anyone else he's sponsoring.
 
Other than that he could be a murderer on death row and retain his right to petition for a relative, although you might have a hard time proving the legitimacy of a relationship with someone who you can only see through plexiglass.

If you want meaningful help here, be open, honest, and specific about real questions that apply to you and your specific circumstances.  If you are evasive and/or ask hypothetical questions, you are likely to be treated like "The Boy Who Cried Wolf".

In the other post the husband is who posts and has an arrest warrant.
 
 
It seems it is a classic case of time paradox. 🤪

Thanks for your reply. This  is another question I'm asking, 

Probably has everything to do with her not having strong ties to her country and that she is married to a US citizen. Not your arrest. How would they know. They are looking at her and if she will return when she is suppose.

Agree more likely the standard 221g

Was she not given a paper at the end of the interview stating the denial? The common reason is 214(b) which is lack of ties to home country or ties to America are stronger than that of home country, such as having a USC spouse.

It depends what the conviction is and if he is eligible to file. I would seek a lawyer. This is not a DIY case.