If you're monitoring the true / false statements within CoRE itself whilst opening / closing the doors, that won't work.
CoRE sets the statement when you first add / alter a condition, but then it only updates the view when you exit (by clicking done) and go back in.
It won't show real time updates in the CoRE app itself.
Write a simple test piston:
Door Contact changes to open
turn on light
Click done to exit CoRE and THEN test
I'm interested in how you setup the second IF check.... May also be a cause of issues.
Can you post a screenshot of you piston.
You can view (and screenshot) a more compact layout of the piston by clicking on 'CoRE Dashboard' at the top of the CoRE main page.
Dashboard also gives you realtime updates and countdowns, showing exactly what each piston is doing.... Helps a lot with de-bugging!
You need to enable oAuth in the IDE for the dashboard view to work.... Let me know if you're not sure how to do this.