From the Amish point of view, it’s providing an opportunity for young adults to decide, do they belong to the world or do they belong to the Amish? Those who return are far more likely to be comfortable, accepting and committed to their unique way of life, and far less likely to create strife, division and dissatisfaction. For this reason it is a practical step for them to take. We are sinners always, so are the Amish, it’s just a matter of degree, and a matter of forgiveness. That’s true of every human being save Jesus Christ himself.
We belong to God. The Bible says that “we were bought with a price.” The Captain of our salvation - our Lord is Jesus Christ - not some Amish leader who sets himself up to be some potentate.
So no, neither we nor they “belong to the Amish” as you said.
We don’t belong to man - we belong to God, although they would like for them to belong to them no doubt.
Yes, as church leaders, they would be within their scriptural right to preach from the pulpit what they wanted to, As in it is a sin to fornicate, but it would be utter arrogance for one of them to say that since you won’t grow a beard, or wear this particular gown or dress, I (as a deacon, elder, or minister of the Amish, or in this particular Amish community) have a right to cast you out.