Sweetcheeksss

No.
You will need to pursue a spousal visa from outside the US, assuming you're already married.
Expect the process to take around a year.
The I-485+I-765+I-131 you filed is now considered automatically abandoned by USCIS.
If you were previously a DACA beneficiary then you may have inadmissibilities to deal with too, depending on whether you had any prior overstay before you were approved for DACA, how long that overstay was, and at what age you were granted DACA.

Tourist bring in billions of dollars to our economy, and spend their money at local businesses. Without this revenue our economy would collapse. We need tourism. We just need to balance that with national security. But telling all potential tourists to watch youtube... no.

Millions of people travel on B2s every year. While it might be ever more slightly more inconvenient than using ESTA, it is not the end of the world. I don't know how it's really unfair to your friend. The US is being very cautious is all. Belgian police and intelligence have done a bad job finding the terrorists among them.

Like others have previously mentioned, have him apply for a B1/B2 visa. Maybe he will be approved.
You asked the question about the ESTA program, you were given multiple appropriate responses, don't shoot the messengers. Whether you agree or disagree with the US government's policy change on the ESTA program is a moot point. Voice your concerns with your elected Federal officials....

Consider reading the DOS link provided in the second response.

He can't get ESTA because of the changes to the rules. But he can try for a regular tourist visa (B2).

http://www.state.gov/r/pa/prs/ps/2016/01/251577.htm
Under the Act, travelers in the following categories are no longer eligible to travel or be admitted to the United States under the Visa Waiver Program (VWP):

Nationals of VWP countries who have traveled to or been present in Iran, Iraq, Sudan, or Syria on or after March 1, 2011 (with limited exceptions for travel for diplomatic or military purposes in the service of a VWP country).
Nationals of VWP countries who are also nationals of Iran, Iraq, Sudan, or Syria.

People are allowed to visit girlfriends. They wouldn't have denied him entry necessarily for being honest. Now he pays the consequences.

This case: K1 visa denied because US consulate found out they were married after filing I-129F petition.
http://www.visajourney.com/forums/topic/493079-k1-visa-denied-to-getting-married/

Why don't you go try it out?
For your information, Some US Consulates actually monitor this VJ website as well, even match the usernames with actual case files

Yes she would, and it has happened before.

Why on earth did you even ask a question when you won't listen to the answers you get?Some embassies even ask for proof of not being married at the K1 interview. This IS a big deal. Low chances of being caught does not make fraudulent and disrespectful behavior ok.

Social media, or a field study where they ask neighbors. If they EVER find out you married before entering your wife becomes deportable for visa fraud.

K1 visas are for fiancés to marry in the US. If you are intending to marry and then get married, then you are no longer fiancés but spouses. You would have to withdraw or cancel the K1 and start over with a spousal visa.

Laugh is you want but this site has actually been mentioned in more than one interview. There are a few members that even admit to working for USCIS.

I don't think you are going to get the answers you want to hear on this website because you are talking to an audience of people who are mostly either
a) desperate to be with their spouse or
b) have made the sacrifice to leave their country which they love to move to America to be with their spouse
So as you have an option of reuniting your family in a pretty decent country - where you don't have to learn a new language and where your job skills will be in demand, and where you can give your daughter access to both her parents - most people are not going to say that's a bad deal.
But immigrating and moving your whole life somewhere new isn't easy for some people - it sounds like it would be a big step for you - so it's okay to be cautious and worried.
What would I do in your shoes?
I would go and give it a really good shot. I would aim to give it five years at the very least. And I would aim to do it with the attitude of really building a home and a life there - and try not to see it as a temporary visit. After five years you would be well on your way towards the possibility of UK citizenship and you'll be able to decide whether to stay on for that so that long term at least you would be able to travel back and forth without immigration issues. Also in five years time who knows what changes US immigration might have gone through. Your husband might have another chance to apply - and at least you would be together while dealing with it.

Reading your post, I haven't once heard you say anything about how your husband feels about all this. He was ready to give up everything for you, yet now when the table's reversed, you're not ready to do the same for him...
Your kid is three years old, she will have no problems moving. Kids adapt soooo easily, especially when they're so young and you're moving to a country that speaks the same language. I've worked in the hotel industry for 15 years, I've seen Directors and General Managers come and go in the different countries I've lived in, they all brought their families along and I never saw any kids have problems adapting to their new country. My family moved twice when I was a kid, once when I was your daughters age and once when I was 8 years old, if anything it made me stronger and more adaptable to change. Sounds to me like you're the one that's scared of moving?!
I understand that you're worried about your elderly parents, especially in the US where you don't have the social safety nets we do in Europe but you must have know this was gonna be a possibility before you started the K-1 visa journey. I mean you did your research before starting the process, right?! You knew it was gonna be hard for your husband to get a visa with his two prior convictions. If you refuse to move to the UK, another alternative could be Canada. Your parents could move up to Seattle and you and your husband to Vancouver, that way you could live together as a family but you would be very close to your parents too, to help them out if needed.
Since you asked for our personal opinion, I'm gonna put it out here; When you marry someone you make a commitment to each other and that means doing whatever it takes for each other. I don't think it's fair on your husband or your daughter for you to refuse to move to the UK. You're basically splitting your family apart and keeping your daughter from her dad. You haven't even given the UK a chance, you haven't even tried.

OP WANTS TO KNOW IF THEY CAN VISIT DURING THE PROCESS.
S/he was asking if they should do the visit first and file later, or if they can file now and visit during.
Yes OP, your parents can visit with a pending petition.

you cannot....not unless you first pay back the many thousands of dollars that US taxpayers spent on your delivery....your son's status as a US citizen will play no role in you obtaining a new tourist visa....you already ignored what was told to you (stay for 2 weeks), the taxpayers shelled out a lot of money, and now you want to be rewarded...it won't happen. Trust is hard to get, but easy to lose and even harder to regain. And B2 visas are all about trust. When a person violates that trust, merely saying 'sorry' or coming up with some excuse as to why the visa holder refused to comply with our laws and regulations or instructions won't restore that trust.

FIrst, the US citizen is committing a crime. Bigamy is illegal in the US. It's illegal for a US citizen to commit bigamy anywhere in the world.
Second, only the first wife qualifies for an immigration visa.
Third, BS on US Immigration allowing bigamists and polygamists to immigrate to the US. Pure BS.

Immigrant Visa for a Spouse of a U.S. Citizen (IR1 or CR1)
You might also want to check out this article (dealing mostly with naturalization though).

Only the first wife would get the immigrant visa -all others are sol.

Section 212(a) of the Immigration and Nationality Act
(a) Classes of Aliens Ineligible for Visas or Admission.-Except as otherwise provided in this Act, aliens who are inadmissible under the following paragraphs are ineligible to receive visas and ineligible to be admitted to the United States:
(10) MISCELLANEOUS. -
(A) Practicing polygamists.-Any immigrant who is coming to the United States to practice polygamy is inadmissible.

I think you are in for a ride if you think you have the upper hand. Prenup is meaningless in regards to the I-864. Not trying to sound like a downer, but why are you making this like a game (especially with the daughter's petition). What's your end game if you already know it's not going to work out between your wife? Divorce and move on with your life.

Coming from Denmark, you have no idea what life is like for people in less fortunate countries.
My cousin's kids live in horrible conditions. There are plenty of reasons to want to come to the US to improve the quality of life for those children. Sometimes, temporary separations can not be avoided. These children are NOT ABANDONED. They are left temporarily in the care of loving family members.