They are setting you up for a huge let-down in April when you get admitted to some colleges, only to find that many of them are unaffordable, or that the 1/3 parental contribution, 2/3 scholarships, financial aid, work, and loans formula does not really work. Also, if they are willing to pay 1/3 of a $60,000 per year college = $20,000 per year, then will they be willing to pay almost all of a $21,000 per year college?
You and they need to run the net price calculators on several colleges of interest to get a realistic idea of what costs you are looking at. It is best if you parents can tell you a dollar amount that they will contribute (e.g. “we will pay up to $20,000 per year” or some such – they need to account for any contribution to your siblings in their budget). Be sure to run the net price calculators for 1, 2, and 3 kids in college, to get an idea of how they may change as you and your siblings enter and leave college.
It is best to start your list with safeties that you know that you will get into and know that you can afford. If you are looking at smaller schools, some inexpensive liberal arts colleges include Truman State and University of Minnesota - Morris. UNC - Asheville (mentioned previously), New College of Florida, and SUNY - Geneseo may also be reasonably priced.
International relations may be specialty area within a political science department; check departmental web sites, course catalogs, and schedules to see if that is the case at schools without a specific international relations major.