I'm not entirely certain, but I think this is a case in which you can actually claim dual residencies.
Different states maintain different standards with regards to who they will consider in-state, but a commonality most of them share is that the parent/guardian's status trumps that of the student. That is to say, if you were to move to a state for educational purposes you'd branded out of state, but if your parent were to move there, you'd automatically be considered in-state when you apply for in-state residence.
If you have the paperwork for New York, and your mom's fulfilled the requirements for Ohio, I don't see why you shouldn't be granted IS status in both states. Pretty sure you're boned for Illinois though, considering most states require a recent paper trail (6-12 months of utility bills, tax info, DL, etc...)
I have strong ties to IL and CO, and have researched this thoroughly.
The primary difference relates to public schools, as the in-state and out-of-state tuition is radically different.
For private schools, a number of IL schools recommended that I write a letter/e-mail that would be added to my file specifying my ties to the state. I was told that this would hold some weight for the many private schools that accept a much higher percent of instate versus OOS candidates.
Public schools have fairly well detailed rules, UIC and SIU have these posted online, and they can be found with a bit of digging. The long and short is that a person must be able to prove they've lived in the state recently for a certain time period (around a year I believe) for reasons not related to education. My roughly 30 years in IL do not establish current residency, as I've lived out of state for a number of years.
Both IL and CO look for a number of factors when considering state of residence, such as state one files taxes in, where one's car is registered, where one has registered to vote, where the person works, utility bills, owning or renting a house/apt in that state. I'd look at your specific state, typically attending college in a state as a dependant (parent/s claim you for tax purposes) will cause you to be considered a resident of your parents' state of residence, not the state in which you're attending college.
IL had a cool exception such that, If I was accepted after applying as an OOS resident, I would immediately convert to instate (and pay instate tuition rates) because my parents live in IL. Maybe other states have similar rules?