There are thousands of people with this same deal that live up North but have Winter homes in Florida. The 10 day deal applies to you becoming a resident which normally means "permanent" resident. If you have homes in both locations you choose one to be your permanent resident, normally the one you spend the most time at. I ran into the same thing several years ago when I was working temporaly in a diferent state.
Key on these factors.
Do you still own the other home
Do you still have the utilities turned on
Does anyone live in the other home
Do you regularly go to the other home
Do you still receive mail at the other address
Where is your car insurance listed as primary address
Where do you vote
Where do you put down as your primary residence for IRS and state taxes (if any)
Where are your car tags listed
All these things are important and if you have homes in CA and ID but move from one to the other you have to choose one to be your permanent address. Just like the "Snowbirds" that move from NJ to FL every winter you don't have to get a FL license if you don't intend to be there for most of the year.