[Lil' Lavery]

Understand that it is within the School's power to restrict the travel and activities of a club/team, especially if it does involve missing school days. A lot of schools/teachers have a problem with students missing that many school days within such a short period (the whole competition season fits in a period of less than two months), especially given the timing. Championship is typically within a couple weeks of the AP Exams, and state testing often falls in the same general vicinity. Be glad you're allowed to goto the NJ regional Week 1 with your NJ state exams the next week. Remember that your education should ALWAYS come first.
That being said, if you feel that you are able to keep up with your schoolwork, its okay to work towards a positive compromise with the school. Don't demand anything, or fight, but stay positive and try to create a solution that satisfies all the parties involved. Given that I don't know your school's specific policies and system, I won't try and suggest any, but that hopefully won't be too hard. And be patient, it may take a few years to win your school over. I find that the best way to get someone excited about FIRST, is to give it to them first-hand. Invite your principal and activities director to meetings, event, scrimmages, and (most importantly) competitions. Let them see what you're doing, and what the events you want to goto are like. Maybe after they witness a regional they might decide its worth letting you miss two more days of school to attend another one.
Also keep in mind, that while there are many teams who do goto two regionals and championship and do well, that doesn't equal instant success (even with a good robot). The wear and tear from multiple competitions catches up to robots rather quickly, and unless your team is experienced at dealing with it, I'd advise you to be cautious when scheduling many events. And the teams that do attend three events may seem like the "norm" (especially among the highly active teams on Chief Delphi), but in reality they are typically much better off than the average team, particularly in terms of funding and the number of participants. Both of those should be factored in when deciding on your competitions, as it obviously costs more in terms of money, but also in energy and commitment, particularly from key members. I've seen many frayed nerves and burned out members after competitions, especially when things don't go according to plan.