As long as QTP is opened before the 3 browsers QTP should create the objects in the OR with the parent browser property of CreationTime = 2 (if you are interacting with the 3rd opened browser as you intimate).
Is this the behaviour you are seeing?
When you say QTP doesn't recognise the page, do you mean the page or the Weblist object on the page?
You can check by running this command:
If Browser("CreationTime:=2").Page("micClass:=Page").Exist Then
Print "Page Exists"
Print "Page Not Exists"