There are several items up in the air here the way I see it.
. At what age is it appropriate to “force” a boy to go to shul
. What is appropriate incentive to get a boy to go to shul before the age of forcing him
. Is missing school an appropriate incentive
I think the answers appropriate for my own sons are:
. 13
. Nothing if he will be miserable while there
. Not for attendance in shul
Every boy is different and each situation should be treated for the unique case that it is.