I won’t tackle the residency question, because that’s best discussed with the school. I will discuss the two-houses issue, from the standpoint of financial aid.
I am not certain that I have this right, but … the home in the city where your kids are currently living is a home you are renting to someone else, correct? If do, that is an asset, and you are required to report the value of that home (market value less any mortgage owed on it) for financial aid purposes. Any rental income would be included in your AGI, so that will also be part of the financial aid reporting (it will be automatically provided by the IRS when you do the FAFSA). Next year, if you have sold the house in which you currently live & take up residence in what is currently your rental home, you won’t report that home as an asset … but if you choose to retain the house you currently live in, that house will become an asset for financial aid purposes.
Basically, you report what is now, and if it changes in the future, you report what is at that time.
Your kids’ residency is completely separate from this, and as indicated previously, speaking to the school is your best bet.