If you are sticking to the main roads a minivan should be fine. However, if you want to get off the beaten path I would go with the SUV. Of course, this is assuming that you are not visiting during the winter months......add snow to the picture and I would say definitely you should have an SUV in that case.
There aren't really any "off the beaten path" places where you can go in the National Parks - vehicular traffic is kept under stick control, you have to stay on major roads.
In my opinion you'll have no problems whatsoever with a minivan.
Its going to be hard to pack 6 people plus luggage into almost any vehicle but the minivan will be fan for anything in the parks.
Good point from Dave... hope you're all light packers...
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