There are regs for everything, and your Personnel/Disbursing office will have the current answers for dual military compensation and benefits, as well as the HHG office for JTR (Joint Travel Regs) entitlements. No doubt there have been changes and adjustments along the way - when I was AD-AD with spouse, at same duty location, we each got single COLA (if applicable) and the with-dependents BAH of the higher-ranking spouse. When we lived in military housing, we BOTH lost BAH, essentially paying double rent. We did get to ship 2 cars and not just 1 to HI. We got the with dependents household goods weight allowance of the more senior spouse, not a double allowance. For one move, we each had household goods allowances on our individual orders, and he was able to move what we had in Hawaii to the next duty station, and I was able to move what we had in storage at a CONUS location to that duty station. We figured that out with the help of a patient lady in the HHG office.
Be extra nice to the experienced civilians or savvy enlisted specialists in those offices, and you will get all the answers and maybe some "tricks of the trade."