SharonTou

Yeah we waited 3 years for his green card so another 3 year wait is a lot , but we are fortunate that we own a home in both countries and have our own business here in USA which he will be working in so we could possibly make this work they will try and see how it all goes thanks Everyone 

I was thinking VWP Express but the original post only mentioned her being here and not the child.

Unless something unusual happens this is going to take a few years.
 
I normally make a comment that he needs to naturalise asap as that will be the quickest way, however he has just got his GC and obviously not through marriage so he is is looking at 5 plus years to naturalise.
 
So:
 
Marry
 
File I 130, I would file I 130 for both unless money is really tight.
 
Be prepared to wait for some years.
 
They can continue to visit but make sure they do not push it with frequency or time.

1.  They marry.
2.  Your son files I-130 for them to start the spousal visa process.
3.  They return to UK before the end of authorized stay.
She cannot legally stay in the US and she cannot adjust status since she is here on VWP (and your son is not a US citizen). 

Green card holders can't petition for a fiancée to stay in the USA. 
Son should marry fiancee and petition her and son using I-130. However, she still can't stay inside the US because she doesn't qualify to adjust status. She'll will have to return home and wait out the rest of the process. Let me stress this, make sure she doesn't overstay her ESTA stay. Good luck.
 

Good point.  Otherwise, her VWP will be gone, and she would, likely, not be able to visit during the process (getting a B@ would be very difficult).

No
https://www.uscis.gov/about-us/find-a-uscis-office/international-offices/united-kingdom-uscis-london-field-office
 
You don't meet the above requirements (both by not being a USC and likely due to residence as well).
Logically that make sense...an LPR must maintain their permanent residence within the US. DCF means your residence is abroad.

Are you wondering if you’re eligible for DCF?  If so, no.