Responses
Not sure prisoner matches. I think he means marriage.
Because that will be the only way that people in the school will understand their relationship because their parents marrying wouldn't mean much, just step-brothers.
But the mother marrying the dad while the two boys marry each other? Yeah, that's a tongue wagging scandal.

The uke was sold off to the seme as part of the marriage between the uke's mother and the seme's father. It was a condition for the marriage, this is literally said. The mother agreed to sell her son to the seme for money via marriage. The seme most likely set this up as he says that he "wasn't interested in public schooling" and that he "just wanted to take a look at your noble figure (the uke)". This implies he knew the uke before the marriage was set up and only attended school there to watch the uke once he was sold to the seme. Now they're both just waiting for the uke to graduate and become the seme's prisoner.