Traveling to US before submitting I-130 form? A tricky situation.

[Porkbun]

Hello!
My partner and I need your help.
We are planning on getting married in the UK, per her family's request, and then moving back to the US.
She is a UK national and I am an US citizen.
We were wondering if we could travel back to the US, after marriage, and then file the I-130.

Previously she had to go back after landing in the US because we didn't have the correct paperwork.
The US embassy in the UK told us to tell Immigration the exact same thing. That lead her to be put back on a plane because we didn't have a fiance visa. We were planning on getting married in the US during the 6 month visitor visa time.

We are worried that if we tell immigration "we got married and now we are moving back to the US" that might make them send her back again and this time ban her from the country.

So long story short...
Can we file the i-130 when back in the US?
If so what would you suggest we tell immigration?

If not can we file the I-130 while in the UK and then travel to the US?
If we do that can we tell immigration we filed the I-130, show some kind of proof, and tell them we are moving?

Thanks for any help or advice you can give!