Welcome!
You are in the wonderful position, if you have not applied for cards in the past 5 years, of being 0/24 in the Chase lingo.
First, the best thing to identify is your goal. It appears (but I could be misreading it) that your main goal is to fly to HI in comfort.
If this is the case then there are people who fly to HI often enough that hopefully they can help-
@wanderlust7 and
@mmmears immediately come to mind-they would both be super helpful in providing United assistance. American also flies to HI and I'm sure there are some people here who are experts in American.
Getting an idea of who flies to HI from DFW and IAH would be helpful, as well (skyscanner and googleflights are your best friend here). It appears AA has nonstop flights to HNL out of DFW, whereas there are no nonstop (but 1 stop) from IAH to HNL with United. You're not limited to only pursuing AA miles though-British Airways can sometimes be used (their availability is less predictable) to fly to HI, as can Alaskan Air miles. United is transfer partners with other Star Alliance partners so you could use other types of miles again with the caveat that sometimes partners don't have the same availability.
I'd decide whether nonstop is important-if so then AA might be the way to go from DFW. If you and DH are open to a connection then this allows y'all another avenue (United and its partners).
Second, after flights, I'd look at hotels-the good/popular/reasonably on points hotels book out early just as flights do so I'd decide which brand (hilton or marriott or hyatt OR an independent and work on cash back) and focus my earnings there.
Once you decided on some of these then I think other people on the board can help chime in to questions like "best way to earn AA (or United or Hawaiian air) miles," "how far out does Hilton/Hyatt/Marriott open availability," " do I need a rental car in X" etc. I could give you basic advice on credit cards but to earn towards HI, I'd be no help at all, lol (Europe yes, thought
).
Hope you find some good information and again, welcome