You need to go to the college website and carefully read the residency rules for your state and your college (what applies in CA may be completely different than in RI, for instance).
Do NOT assume that you can go to Mom's New State and be considered a resident there. Many states are quite picky that resident rates go to students that have attended high school in that state (it won't be worded that way but that's the way it is structured).
Worse case scenario: you are considered Out of State in two places! Sorry, but you really do need to read the residency rules for each state and, further, for the colleges where you might attend. It is far better to master these details now, before the move because thousands of dollars could be at stake.
Not only would I read the RI and Future State residency-for-tuition purposes rules very, very carefully, I would also write or email the Admissions office and say "this is my understanding of these regulations. Do you agree?" so you have a written response that covers you with that college. (Don't just call and chat. Get it in writing).
States are really, really broke. In my state, WA, we suddenly are 90 million in the red. Given those realities, you can count that colleges are not going to be generous -- if they can count a student as OOS, then that means another $10K/year in income.
So it's a good thing you are asking questions now, before Mom moves. Go ahead and conquer the details and then you can both move forward with confidence.
People are not heartless. If Mom is moving to take care of Grandma, for instance, then go ahead and ask what it takes for you to retain in state status (should she keep a PO Box? File her taxes from RI?). The answer may not apply for all four years of your college career, but it could save you some big bucks if you timed things right (for instance if she was going to move in late May but the residency rule says "must live half the year in RI" then her bumping the move back to early July might save you $10K for that next school year).
The devil is in the details. Be careful and very, very knowledgeable.