Hi Daysha! Extra planning needs to be done for any vacation with a toddler in the family. Happy children make happy parents and that all makes for a happy holiday!
If your two year old needs a nap each day to keep on a schedule I highly recommend you plan around that and head back to your resort or condo. You can even incorporate some pool time in for that break of the day making it extra fun. The parks all have a
Baby Care Center for guests to use but these are primarily designed for feeding, nursing, and diaper changing. They really don't have cots for napping and they are not completely quiet as guests come and go. Finding a quiet spot in any of the parks is hard as well for a stroller nap. If a good nap is what you want then it is best to head back to your room.
Since you are traveling with a little one you might be interested in something new at Disney called
Kindermoon Packages. These are designed for the families who want to come for a vacation but are bringing the youngest family members. They have developed special packages that include special vouchers and activities that are included in the price. If you have not booked you might want to take a look at these.