Are there reasonable hotels for a family of 9?

Yes

We stayed at the Millennium near Duke. It was very nice and not too far from everything

There is Candlewood Suites. I'm not sure if there are rooms with family rooms. But these are kitchenettes, and they are clean and do not have carpet. I found my best rate online thru 3rd party

I'm not sure about the hotels in the area.

In Morrisville there are stay home apartments