You’re son is braver than I was. I don’t really like foreign objects getting put into my body (I pass out about 50% of the times I got for a blood test). But I always wanted a tongue ring. The one time I pulled myself together and decided I would go get it, they were closed…
I wonder if the question is whether you have the right to tell him that he must be Shomer Shabbos in your home or not. You explain that you want your home to be Shomer Shabbos. Do you ever have a goy come over to do something for you on Shabbos? Can a pile of Jerusalem stone be Shomer Shabbos or do you think you might be trying to rationalize the pain of your son’s open desecration of what you hold dear?
I once called up R’ Avrohom Shorr because I was at my Mother-in-Law’s house and my wife is the only one who is Shomer Shabbos in her family. I asked him if we should go away for Shabbos (I think it was Shevuos also that year) because the chillul Shabbos was really bothering me. He told me that I should be l’maaleh min hamakom and l’maaleh min hazman and stay. Shabbos is what we make of it. All the Rebbeim in the YEshivah I went to in E”Y were all exposed to chillul Shabbos and I never heard of any of them saying anything to anyone about it. They made their Shabbos and were happy just to get us to come to the seudos.
I’m not saying that the right answer is to ignore your sons actions. You have other children and need to measure the impression of your sons behavior on them. But maybe you can modify your reaction to his behavior in light of these thoughts to be more calm and accepting of him during this struggle. The more that you express negative emotions to him, the more he will feel pushed and run the other way. The more accepting you can be of him in your heart, ?? ?? ????? ???? ????, the easier it will be for him to run towards you.
Maybe it would be effective to say something along the lines of:
We understand that you are already 16, an adult that is mature and free to make your own decisions. You are your own person, responsible for yourself and have the right to choose whether to keep Shabbos or not. But there are other impressionable children in the house that are our responsibility. So maybe we can agree that you are free to come and go as you please, but any chillul Shabbos that you feel you need to do, you do outside the house. In this way we respect your freedom and none of us have to worry about the effect of your actions on the children.”
In this example you are validating his “maturity” both by “admitting” that he is an adult and by separating him from the “children” of the house. Then you are using the positive feelings that this evokes in him as a base to propose your “trade” with him.
And most importantly, don’t make your family’s Shabbos revolve around the actions of the boy that is troubled, but about reinforcing positive feelings in your family.