I've downloaded and tested your adpTest.zip
In that source you are using the same adp twice. The first time you assign the adp to sDate and the second time you assign the adp to eDate.
When the user click on the 'Set Date" button, the adp is shown, but the result will always be send to the eDate which is currently linked to the adp.
You need to use 2 adp and link adp(0) to sDate and adp(1) the eDate.
Sub Globals
Dim adp(2) As AnotherDatePicker
.... more code here
End Sub
Sub Activity_Create(FirstTime As Boolean)
....
adp(0).AddToActivity(Activity, VM1.GetView("sDate"))
.....
adp(1).AddToActivity(Activity, VM1.GetView("eDate"))
....
End Sub
Sub sDate_Click
adp(0).Show
End Sub
Sub eDate_Click
adp(1).Show
End Sub