You should not have problems when moving tests that are used as test as steps in other tests if you do it using Test Studio interface. If you move files using Windows Explorer, the connection parent to child (used as test as step) test breaks.
Here is some info how Test Studio updates files in remote execution, which can help you understand why it doesn't always work at your end.
When you create a scheduled remote run first time, project files and tests in the test list, including tests used as tests as steps are uploaded to MongoDB database, from where they are downloaded during scheduled execution by the Execution Servers. So if you create a remote scheduled run, all files get uploaded to the MongoDB. If you then move or make changes to any of these tests, after saving them, if you trigger another remote run, we check if the files already uploaded into the DB are older than existing ones and re-upload the changed files. What you describe can happen if the parent test is not changed for some reason, but child test is changed and it does not get re-uploaded to db, so it fails to find it upon execution, which can happen only if tests are copy/pasted/moved using windows explorer as per our knowledge.
What I can advise you is to drop the MongoDB
and create a new run, this will upload all needed files properly.
If you face similar issue again, please let us know exactly what you did in project like copy/paste/move of tests before the problem occurs.
Thank you for your feedback and cooperation.