When you manipulate data from a database, it is assumed that you know the database, or you would not know what you are doing.
Disable the constraints temporarily resolves? I do not think then you'll have to call back then anyway you can not have corrupted the records relationship.
That is: you do not escape knowing what you are doing, you need to know the relationships beforehand and you need to know the implications of excluding a record with dependencies.
The most meaningful option for me is delete the records in the order of your dependencies, first the children and then the parents instead of pretending to ignore these dependencies.
You can still bulk delete: delete the 1500 child records, then the 1500 parent records and then the parent records, and so on.
If deleting dependencies when deleting a parent is a default procedure for these tables, then I have the Math option: change the table to make the exclusion of dependencies automatic and permanent.
Now, if you do not really care about the data
If you are for example using a test database it may be applicable from time to time to exclude records and destroy dependencies as if there were no tomorrow.
In this case an option is a script that retrieves the metadata from the table and traverses the dependencies by deleting them in the correct order.
This script can be a client-side wrapper code in the language of your choice, or a stored procedure.