UNHs site "Residency is determined at the time of admission for degree students "
That means it is decided there and then, there is no language that indicates this is changeable. Some states to decide this status once only. Your appeal needs to be clear that your parent was a resident at the time of your offer. Again, what did your offer letter state?
From the UNH website…
If this mom moved in June…this mom would not have resided in NH for 12 continuous months “prior to the term in which in-state status is desired”.
And the student is a dependent student for tuition purposes.
“6.5 When a person has established eligibility for in-state tuition based on his or her parent’s domicile and the parent subsequently establishes domicile outside of New Hampshire, the person shall be eligible for in-state tuition for one academic semester following the academic semester during which the parent established out-of-state domicile. The student shall notify the campus residency officer of any changes affecting the student’s eligibility for the in-state tuition rate, pursuant to BOT IV.E.13.”
This seems to be the thing the school is citing then. Still appeal, IMO. Call. But have a plan b. You could construe this as giving you instate tuition for the year, or just a semester. If it is either and your appeal is denied, IMO you need to not matriculate. Take a gap year and go where you are instate. Are you talking to your mum about this? It is a very significant issue.
the post office notified them 
@Sybylla what letter? my acceptance letter or the email they sent me notifying me that they are going to change my status to out of state?
It sounds like you’ll only be considered in state for one semester – if at all. Can you move to Maine with your mom and attend college there?
You need to discuss this with UNH. Every public university has guidelines for instate residency status. You will need to adhere to those.
It sounds like something was mailed to your NH address and was returned to UNH. Or something. The PO would not have sent UNH a new address…but they would have returned to sender anything not deliverable.
I agree that the language “Residency is determined at time of admission” is key to the OP’s chance of a successful appeal. Then further language would maybe give the applicant a chance at two terms of in state tuition. After that, it’s OOS rates. But by then Mom might have established in state residency long enough to get Maine in state rates if OP chooses to transfer.
The flagship schools do tend to dig in their heels for matriculating students. Getting accepted as anIn state student does not mean you get in state tuition rates. I’ve seen many fights over this. It’s a disgrace that universities cannot write very clear tuition policy in this regard and stick by them. But that’s what I’ve seen too many times.
Put up the good fight— you have good advice on what to use, but prepare to find yourself having to choose between paying OOS or finding a less expensive school. Even if you get in state for this first year, It’s going to be difficult to continue getting in state rates. It’s clear that the parents ‘ state of residence is what is considered the state of residence for the student.
If OP has to transfer they won’t be eligible for freshman grants. Unless her parents can pay out-of-pocket her last 2 years she needs to make sure she starts at a college that will be affordable for all 4 years.
What are your stats? Major?
Are you calling and talking to people? Started the appeal?