You are not presented with any linking options when you want to link a child ticket to another ticket ( I have realized that you are calling a relation between 2 child tickets as "peer child tickets" ). The button at the bottom of the sidebar reads as "Unlink Ticket from Parent". This both creates some confusion for the agent and also prolongs the linking process because you first need to switch to the Parent ticket and then you also have to have the authorization to link a ticket from another department etc.

Please consider a more straightforward linking process. There seems to be a limitation at parent-child linking level where it's set as just 1 level ( Parent and Child). Either consider presenting more levels or as I have proposed before on this post ( Parent-Child Ticketing: Additional Link Type request) introduce a different type of linkage.