VLookup With 2 Criteria - Provide Log Of Staff Allocation

I'm fairly new to excel and trying to create a simple spreadsheet to provide a log of staff allocation. I've created a first a sheet displaying a table with a week of rota. The first column lists where the staff are placed, the first row the date and inbetween the staff member covering that date. There are 5 further sheets, one for each member of staff with a simple table - first column is date, second is allocation.

Back on the first sheet below the timetable is a further grid showing on the first column staff names, and below each date a formula =VLOOKUP( B$3,David!$A:$Z,2,FALSE) pulls information from the 5 sheets displying whether a memeber of staff is on leave or there allocation on that particular day.

The problem i'm having is trying to get the 5 simple staff sheet to pull data from the Rota ie. I need say B3 to look at the date in A3, find the same date on the Rota sheet, look for the relevent staff name below it (if present), and display the allocation from the first column on the same row as the staff member.

I've tried a combination of Vlookup with Match and Index with Match but nothing seem to work.