Are there actual laws written, or de facto situations (e.g. let's say
another law specifies that a child can't be physically forced to go
anywhere without causing abuse) where the child can refuse to attend?
Are there "tiers" to the age; Is it true that a temper tantrum of a 5
year old would be seen as such, but the refusal of a 17 year would be
legally accepted?
This is a hard question to answer that doesn't have a neat resolution.
Very little pertaining to the authority of a parent over a child is codified in statutory law and there is not a clear cut age at which a child has "freedom of conscience" vis-a-vis a parent.
Most of the law related to children concerns allocation of parenting time and parental decision making between divorced, separated or unmarried parents; abuse and neglect; and juvenile delinquency. There is also usually a snippet of criminal law stating that certain kinds of uses of force to discipline children do not constitute crimes.
But, part of why it doesn't come up very much is that older children are usually socialized in a manner that causes them to show a certain amount of respect for the wishes of their parents. It also doesn't come up much for children who aren't in their late teens, because the complete economic dependence of children on their parents or guardians gives the parents considerable power of their children that doesn't require the exercise of physical force.
Also, it is quite dependent upon how the issue presents itself. No law enforcement agency is going to aid a parent in forcibly dragging a kid to church against their will. But, no social services agency is going to remove a kid from a home because his birthday party will be cancelled if he doesn't go to the church of his parents' choice the Sunday before his birthday.
There are also some subtle but important distinctions between states on the issue of emancipation.
In Colorado, emancipation is a statement about the empirical reality. If a child is self-supporting and lives apart from parents or guardians then the child is an emancipated minor. It is not a status granted by a court, it is a status acknowledged by courts when evaluating other issues.
In California, a child is not emancipated unless a court grants a child that status and a child who is de facto emancipated without the leave of a court is guilty of a "status offense" (the New York State term for someone in this state is PINS for "person in need of supervision").
Basically, if a parent can force a child to go to church by means that don't constitute abuse or neglect and don't exceed the level of force authorize for child discipline in the criminal code, then they can do it, and if they can't manage that, then they can't do it.
Many states have a "status offense" that allows government intervention with the cooperation of a parent or guardian in cases where an "uncontrollable" child is defiant and simply will not give any heed to the parent or guardian's instructions.
In practice, the older a child is, the less likely someone viewing a parent's conduct forcing a child to do something is to be viewed as acceptable or legally justified.
The legal rights of children in a school setting are also age dependent under the case law, although not always in a really well defined way. Controls on student expression that would be uncontroversial for elementary school students may be looked upon by the law with disfavor for high school students and clearly prohibited for adults.
Perhaps one useful way to conceptualize it is that trying to make a child attend a particular kind of religious service is not considered an improper purposes for a parent of any minor to utilize the resources available to the parent to do so, but the range of resources available to a parent with regard to an adult child is much narrower.
