Redirect where both source and destination are the same

Hopefully I'm explaining this well. Recently got a requirement for a particular set of applications. So lets say traffic comes in.

Traffic -> Pool A and randomly selects server 2.2.2.2 Traffic with particular uri -> Pool B, but the traffic should still go to server 2.2.2.2 which is also in this pool.

The traffic would be within any given user's session. Server 2.2.2.2 would be in both Pools A and B. This would need to be done dynamically. Whatever server the user originally hit when they went to Pool A, would need to be the same server they hit when they're redirected to Pool B. The reason for this insanity is that they have two apps that originally shared the same directory on their servers, but they're migrating one of them, so it will now reside on a different directory, and the developers don't want change the code because the app is 15 years old, and this is supposed only be a temporary solution(5-6 months).

Anyone know how I'd approach this?