1031 exchange from my LLC to personally-owned second home

I just relinquished two rental properties which are owned my by single-owner LLC. I am wondering if I can do an exchange with my second home, which is owned by my wife and I personally. I understand you cannot 'exchange' a property for one you already own, but I wondered if there is a distinction since my LLC would be purchasing it from me.

Thanks in advance for you advice.