The simplest way to know which state you should be applying to is not where they own a home, but where they pay taxes and vote in. It is called their Home of Record (HOR)
If the HOR is in a different state many MOCs will either do a telephone interview or Skype.
For some states there is a loophole. Just because one parent is AD, it doesn't mean that the spouse and children are residents of that state too!
Our DS was considered a NC resident because we also paid personal property tax and required me to get an NC drivers license. If a car is registered to a military dependent in NC it is taxable. If it is registered to a military member only it is not taxable.
That changed everything for our DS. He was eligible to request a nomination from AK, his Dads HOR OR NC where I was considered a resident due to their requirements. However,see my first point....taxes.
If I declared him on my NC tax return, he could not apply for AK.
We spent hours contacting the MOC staffers in AK and NC and all of them said the same thing. It didn't matter where his drivers license was from, but the state taxes for him as a dependent.
It gets muddy if the folks both work and are like us, pay state taxes for one parent while the other is exempt and you have a DL in that state.
Do what we did, contact all of the 3 MOCs in each state and ask them directly, you are not going to be the first that has asked the question, and they know the regulations for dependents of military members.
Good luck! JMPO, but on a whole I think you will be classified as a resident of where they vote not where they own a home.