fwiw it sounds to me like you are doing fine. The confusion about Trinity likely exists because Trinity is just a doctrine of men anyway, mostly used to divide people; you don't have to accept other peoples' concepts about God, even if they wear a tie and have charisma and signed a Contract for Jesus, ok. 65 million people have left that system already, where prayer is defined as something you do on your knees with your eyes closed, and there is a list if boxes to check to consider yourself saved. Those are not "church" anyway, you are the Church.
Your son is likely just claiming "Atheist" as a rejection of either that or you, and the parable of the Vineyard Owner with Two Sons should be considered there imo. If you do what God does, and just ignore or even signal acceptance when you hear "atheist," rather than offering resistance, recognizing that people say things for lots of reasons, but they only do things they believe in, then a lot of your anxiety about effecting change will likely go away. You are a father, so of course your behavior has an effect on your kids. You are seeking God, and have quite naturally gone to the societally accepted place to further that search, and i suggest that your kids maybe just detect some hypocrisy that you are blind to there.
i know this is hard to contemplate, having been raised to believe that God is wherever "church" was, but even your syntax, your lingo, ends up framing God in a religious perspective, rather than maybe a more daily-use or moral one, and i can tell you that the people that have never told you about the baptism of fire--because they do not even know what it is--are not the best ones to be emulating in your speech anyway. God has no interest in a religious relationship with you.
see, you go there to talk about sin and death, right, and what you life will be like someday, after you die; and this does not comport with God's plan, to bring heaven to earth, with you as the Body of Christ. So there is a basic misunderstanding, mostly centered around a bad definition of "eternal life" imo, which i'm not sure but i'm currently thinking God means that collectively, whereas we are of course absorbed with where we, specifically, will land after we die; almost surely a moot point, that can only end in judgement of others, which imo is why that is presented in the way it is in the Book.
Basket Case in the mud is a pretty good perspective imo--if you get much better, see, then you will be no use to God. You start being assured that you know things--contrary to Scripture--and might even start believing you can tell other people how to get saved, lol.
