Thanks for your reply.
You are right about the SSIS / data tools.
If I start data tools (or start visual studio 2010, which is I believe the same), start a new project, choosing integration services / integration services project and then << OK >>, this gives me the message "Microsoft Visual studio is unable to load this document. To design Integration packages in SQL Server Data tools (ssdt), SSDT has to be installed by one of these editions of SQL Server 2012: Standard, enterprise developer or evaluation. To install SSDT run SQL Server setup and select sql server data tools."
When I installed Enterprise the Data tools selection was already chosen, but I could not change it. It was "greyed out" so to speak. I tried to do the installation another time (and hoped that I could change this field it wasn't, again, not possible (so I left this process)
For your question about integration services being listed and running:
SQL server Integration services 11.0 is running and starts automatic.
Can you use this info for my problem?
The reason why I hoped that uninstalling both instances and installing Enterprise again is that, prior to installing Enterprise on my "regular computer" I did a "test installation" (just to see what happened during installation) on a test computer and there SSDT / SSIS / SSAS and SSRS work fine (that computer has no Express instance installed)