Are you or aren't you responsible for the spirituality of others?
Your position is ironic to the Nth degree and it's sad and quite telling that you can't see that.
No, what's sad is your confusion of fact, Halacha, and nice vertlach taught in first grade.
A. Arvus means that in terms of certain dinim you are responsible for another.
B. In a greater sense it underlies the notion that each Jew is responsible to ensure that each other follows the Torah.
C. This concept is not brought down concerning "kiruv" by the Rambam or any other poskim. Thus, being that were religious Jews, we stop and say the following: "Though I'm really smart and I can figure out how to rack up 1 million points, the poskim didn't take my great genius to the next level to codify Halacha as such. So where did I mess up?"
Hint: Mostly the din of arvus is related to halachos of mitzvos and tochacha (rebuking).
In summary, arvus as a technical matter applies to what the poskim say it does and that's it.
D. Even if you want to relate it to to the Lakewoid story, how should it go? I say focus on your kids and on the frum community and show them that mocking shemiras Shabbos is unnacceptable. You say to be mekarev the kids. Who said you're acting with arvus more than I am?