I think you are just looking at part of the process for the I 130, 18 months or so would be more nominal.
I 134a just not enough data to comment on how quick, just a lot quicker.
The issue is getting through the system, I have always assumed the actual doing something is minimal
I remember my interview, pretty sure this was the first time he had seen the fike, I was watching, 20 minutes until I had visa in hand
Perhaps I am being pessimistic and I certainly am not suggesting you do not try everything but the US Gov definition of speedy very seems to match with the normal meaning, so let's assume they do pull out their finger still might not meet your timeline
Best case would be that you are close to it coming through and it comes in a few days but no way of knowing now
Are you looking for her to arrive after you are back in the US, I would have thought being deployed means you have by definition a US domicile and possibly residency
I have been trying to think of comparable cases for K1 etc and the only ones that came to mind were national service and that did not meet the requirements
I know this is not true but theoretically this program is for people needing to flee so you are putting a case together where everybody is sort of in the same situation
So what would I do, the safest option is to focus on leaving asap, I would think there are a few places that would allow this, should be easy to find out and pick one
I am in a brain fog obviously my first thought is that there is time for parents to naturalise and petition sibling before 21
Or consulate processing as child of LPR before 18 1/2
They can not adjust and seems like they would be subject to a ban on leaving
Are there any qualifying relatives to file a waiver?
There is an exception if you are in the Military
When she gets here which is a long time in the future she can sponsor her eldest daughter assuming she has not married.
otherwise she will need to wait until she becomes a Citizen so she can sponsor her and her family.
obviously when looking at these really long time periods things can change but we can only comment on the rules as they are now