Does 1Corinthians 15:26 include the second death? Some might prematurely try to say "no" because it's a death induced by God. However, I believe that God was more bringing a seed to harvest (i.e. wages of sin) than executing a sentence. If we say that death is an enemy, then which death? Some would say "physical death." But physical death, in the way that many people look at it, was induced by God after the Garden of Eden incident. So, we have both physical death and the second death being induced by God, and both of them are with regards to the wages of sin.
So, if God is inspiring His Apostle to say that death is an enemy, then it's more about what was behind that death (i.e. sin) than about God's alibi with regards to individual deaths. The last enemy to be destroyed is death, whether the first or the second. There's no separating that from the context of the passage in 1Corinthians 15 where previously it was said that "As in Adam all die, even so in Christ shall all be made alive." The whole chapter is about the mortal and the corruptible putting on immortality and incorruption.
And of course, some try to get cute with 1Corinthians 15:22 that "only those in Christ shall be made alive," as though there were two separate classifications. Perhaps there are in our daily experience, but not in the understood apocalyptic language of St. Paul with regards to these matters. Romans 5, 2Corinthians 5, and 1Timothy 2 explains 1Corinthians 15:22 that as all were in Adam when he died, and therefore all died because he died, even so all were in Christ when he died, and therefore all will be made alive because he died. When you compare all of the different relevant passages, that's what you're faced with. People get confused about the one and many equaling the all language of a few passages of Scripture in the Old and New Testaments. But that doesn't change what the Biblical teaching is, just because they're confused by it or have contrary traditions or peculiar paraphrases that they're trying to pass off as translations of the 2000 year old text.
Death is evidently death in Scripture. I've yet to find where there's a distinction between the first and second death. They're both because of sin, and they were both put into place to curb sin's nature and effects by God. The Old Testament is full of practical lessons on how to prolong life and delay physical death. The New Testament is full of practical lessons on how to not be hurt by the second death. Seems like from cover to cover the Bible's teaching how to avoid death. Some want to say that death, in it's ultimate sense, is separation from God. The shell game with definitions, whether that's the correct interpretation or not, doesn't change all of the Bible's language with regards to death, such as in Ezekiel where it says that God takes no pleasure in the death of the wicked, but that the wicked would turn from their wickedness and live. Some want to say that death, in it's ultimate sense, is destruction. Psalm 90:3 and Psalm 103:4 both say that God reclaims people's lives from destruction.
(It says in Ezekiel that God takes no pleasure in the death of the wicked, but that the wicked would turn from their wickedness and live. It says in Isaiah that God's counsel shall stand and He'll do all of His pleasure. Hmmm...)
Ephesians says that God brings to newness of life those that have been dead in sins. That's not a play on words or a twisting of Scriptures. To me, that applies to what can be termed the first fruits and the latter fruits of redemption. I'm getting long-winded again and don't want to write another essay for as long as I live! Hopefully I've said enough to illustrate my point that 1Corinthians 15:26 includes the second death.