What do I do if I live full time in WA, but received income as part of the sale of a childhood home in NY? I already filled out NYS IT-2663 and paid estimated taxes.

For this sale, I had 1/3 ownership of the home. When I enter the #'s for 'Net Proceed' as well as the  'Cost Basis', would I divide both 'Sale price less selling expenses' (line 15 on IT-2663) and 'Cost or adjusted basis' (line 16 on IT-2663) by 3?

The estimated tax that I paid to NY was based on 1/3 ownership. i.e. on line 18 of IT-2663, I followed the instructions for "two or more persons transfer or sell the real property..." and divided the total gain by 3.

Yes, you would report 1/3 of the sales price and the cost basis for your share of the gain on the sale.

This sale needs to  be reported on your federal return.It will transfer over to your Nonresident NY return, and the Estimated Tax Payments that you paid on the NYS IT-2663 will show as a credit. 

In the Federal section:

1. Report this as Investment income, under Stocks, Mutual Funds, Bonds, Other.
2. Say that you did sell investments in 2017, and you did not receive a 1099-B. 
3. Under Choose the type of investment you sold, select Everything Else.
4. On the next screen, you could describe the property as “House”, and enter the net proceeds and the date of sale.
5. On the next screen, check that you acquired the property as an inheritance, or as a gift, or whatever the circumstances were. If you inherited the property, your cost basis in the property is the Fair Market Value as of the Date of Death. If this was a gift, your cost basis is the cost basis of the giver.
6. Continue through the prompts.

For this sale, I had 1/3 ownership of the home. When I enter the #'s for 'Net Proceed' as well as the  'Cost Basis', would I divide both 'Sale price less selling expenses' (line 15 on IT-2663) and 'Cost or adjusted basis' (line 16 on IT-2663) by 3?

The estimated tax that I paid to NY was based on 1/3 ownership. i.e. on line 18 of IT-2663, I followed the instructions for "two or more persons transfer or sell the real property..." and divided the total gain by 3.