I just returned from 3 weeks in Kaua'i. I've spent quite a bit of time on every island.
I adore Kau'ai (and returning again soon) but around the 2.5 weeks mark, I start to get island fever and want to go home. I start finding myself driving around the island in circles. Hearing the same songs on the radio, everyone driving 30mph and slow pace starts to wear on me.
3 weeks is lovely, but one of you may get island fever. I personally would only do 2 islands in 3 weeks.
I'm a business owner and the "hang ten" / aloha spirit is amazing for a few weeks, then I need to return to the mainland, hustle and bustle, tall buildings and seasons. I am ready to go.
Hawaii is a like a long-term romance, you have to find what works for you and it takes a few trips before you find your fit.