Is it rude to take all the time allowed to make an offer decision?
Not at all. You should go to the interview, see the competing offer, if you get it, and then decide. Note that you will likely not have time to have either school make a counter offer. Therefore, I would recommend that at the interview you let the school know you have an existing offer and deadline and that they will have to move quickly and at least match the other offer (or whatever it will take to get you there).

If the school that has made the offer asks, just tell them you are waiting to hear from one last place. You could send a preemptive email telling them that, but there really is no need.