Hi Anup,
I think that six full days is plenty of time to cover the four major parks. Remember, if you do not cover every attraction or show, you can always come back. I think many guests, including myself the first time I took my children, forget that you do not have to see everything. Knowing we can always return has taken the stress out of touring.
As for naps, my children would nap in the stroller so we never came back to the resort in the afternoon. It was also because my children at that age were generally in bed by 8-8:30 and coming back to the room would only reduce our time in the park. Plus we would rather make sure the girls would sleep through the night and have a little down time ourselves in the evening so we did head back for a nap.
There are quiet places in the parks to sit and get out of the sun. There are baby care centers at all the parks which can provide a quiet spot. You can also ask the cast members for recommendations.
You can also hop on the bus and head back to Pop Century as well. From here you can then head out to an evening of fun.
I recommend you stick to your 2 1/2 year old's schedule as that makes for a happy child.
Wishing you a magical vacation!
Beth