You can read a more extensive background about John in the 1 John 1 post: HERE. This was written about the same time as 1 John, A.D. 90, from Ephesus.
We do not know if the "chosen lady and her children" are an actual mother or symbolic representation of a local church or group of churches and the members of the church or churches. Female personification was common in Scripture (Ephesians 5:22-33; 2 Corinthians 11:2; Revelation 19:7). I think it is the later interpretation because he drops the use of the singular number for his pronouns after verse 5.
John warns against the antichrists (false teachers) who denied the person of Christ and His incarnation (2 John 7; 1 John 2:18, 22-23; 4:1-3). They were not even to show hospitality to them. He also emphasizes obedience to God's commands, especially the one to love one another (2 John 5-6; 1 John 2:3-9; 3:14-18, 23; 4:7, 11, 20-21). In many ways, 2 John is a shorter version of 1 John.
John's children were to love (v. 1), walk in (v. 6), and remain in (v.9) the truth. Love will be the main result of this!
Set some specific goals for loving, walking in, and remaining in the truth for the coming year. Your Bible Book Club journey is almost at completion. What will be your goals for staying in the Word and applying it after the BBC is all over?
Lord, help us to discern truth from error and to walk in the light of Your truth by loving others. Amen.