The longhouses with the bigger rooms are Tahiti, Rapa Nui and Tokelau, but honestly ALL of the rooms at the Poly are very large. As luck would have it, these are also the only 3 longhouses with balconies on both the 2nd and 3rd floors (all other longhouses have full balconies on 3rd flor and faux balconies on 2nd floor). The only longhouses with double sinks are Tahiti and Rapa Nui, but of the 3, Tokelau is the most centrally located, and therefore has A LOT of love from DISers. Tahiti and Rapa Nui are very close to the TTC, but are considered by some to be just a little too remote from the GCH and the main pool. Of course, everything is relative, and how you perceive the distance could be related to how mobile your family is and how the weather is during your stay!
With regards to patio or balcony question, lots of families with younger kids prefer the patio; it provides more space, and you can walk out and enjoy the grounds from most patios (some are enclosed by close-lying shrubs). I personally prefer the balcony for the view, but I don't have younger kids.