It is common for students to want to go away for university. It is also common for this to cost more. Each family needs to decide what they can afford. A lot of students stay in-state because that it what they can afford. Admissions is also sometimes more predictable in-state.
I think that it might be worth sending in an application to U.Mass Lowell even if the preference is to go elsewhere. When the time comes it is good to make sure that you will have an affordable acceptance.
I would also be tempted to send in an application to UNH. It is a good university with an international relations program and a very attractive campus. It is also out of state but not too far from Massachusetts.