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Yes. You have to pay capital gains tax on the sale of the 2nd home. There's no way out of it either and what you did with the first home doesn't matter.
In order to qualify for the capital gains tax exclusion, you must have lived in the property as your primary residence for at least 2 of the last 5 years you owned it. You only owned and lived in the house for 11 months. You flat out do not qualify for any capital gains tax exclusion and 100% of your gain is taxable income to you.

If you qualified for the exclusion on the house you sold in 2015, you should amend the return and take it.  There's nothing you can do about the 2016 sale unles the reason you sold it so quickly qualifies for some type of exclusion.

The 2016 sale will never qualify for the full exclusion. The only way it would qualify for "any" exclusion percentage, would be if you sold it because you moved under military PCS orders, or moved as a condition of employment or continued employment. From reading the original post, this "sounds" like a planned event with the intent to make money while reducing the taxes on that money. WHile money was made on the sale, taxes were not reduced. It's called the "school of hard knocks" and we've all attended it - and have been enrolled multiple times even. At least next time, you'll know.