Qrew LegendI don't believe you can dynamically control whether a user will see the Add parent button. Of course, you can set the user interface to disable the Add parent button, which will also disable it on the record picker while still allowing them permission to create a parent. That does mean that you will have to give them a button somewhere to let them create a parent when there is a legitimate need. That may have to be on the homepage of the app because once you suppress the Add record button, it will no longer show on the Table homepage.
One other option, however, is that you could use Formula Query on the parent record form to detect if the Parent record already exists. A formula Query can compare the input that the user has done on the unsaved Add Parent form with existing records in the database and thus you can dynamically put up a warning to the user so they know they are creating a duplicate and of course you could also have a form rule to abort the save. Also, you can also set a field on the record as being unique or formula field is being unique, which would also have the effect of blocking the Save. Blocking the Save after the user has done a bunch of data entry is not particularly friendly to the user, but that might be a last resort to prevent duplicates.
