Summary of the comments which led to a solution:
I first suggested checking the Precedence Constraints. My bad as the question clearly states SQL2008R2 and these didn't come along until later (2014?).
However I also suggested using Sequence Containers.. which seemed to do the trick.
I'll try to post a link to the docs in a moment and apologies if any of this turns out in Greek (phone is having a funny moment)
Edit...here's the link, Tips and Tricks for SQL-BI: Sequence Container in SSIS