Is it too late to quit the part-time job? and let the school tell the officer that actually he quitted long time ago, however we forgot to withdraw the H1-B????
-Do you still get paid? If no, your school can say you have quit the job already.
Do you really work for the part-time job at the working site? If yes, you will be fine. You had better find some excuses on how to do work at this working site such as you work one day a week or 4 days a month, or work weekends, etc. Had better discuss with your HR Director and your supervisor before you meet the IO so that all of you can be consistent to the answers.
What kind of TROUBLE? Please help and clarify it!
-Your employer may be fined and your H1 status might be invalid. But this is just my guess and perhaps you may be OK.