Contemplating 1031 Exchange - Is this possible?

[Nate B.]

I own two homes, one of which is my primary residence, and the other being an investment property, currently being occupied by my parents. They have been paying us a minimal amount of rent over the past 2 years, while living in our investment property.

My parents' health has been deteriorating and we're planning on having them move in with us, as to have them closer and provide the care they need. Ideally, I would like to sell both homes, and build a new home that has an in-laws set-up, where they would live. 

Is it possible that I could do a 1031 exchange by selling both homes, use the proceeds from both sales toward the purchase of a new home, and defer the recognition of capital gains and related federal income tax liability on the exchange?

Thanks in advance. Nate