I am not disagreeing with David at all, just being precise re a couple of aspects of the change.
If you have implemented reasonable standards, then the only code affected with be code that addresses the changed columns in Child (not New_Table). If you have not, then an unknown amount of code, which should not need to change, will have to change.
The second consideration is the quality of the Primary Key in Child. If you have Natural Relational Keys, the addition of New_Table has less impact, not data changes required. If you have IDENTITY type keys, then you may need to reload, or worse, "re-factor" the keys.
Last, introducing New_Table is a correction to a Normalisation error, which is a good thing. Consequentially, certain Child.columns will become New_Table.columns, and New_Table can be loaded from the existing data. You need to do that correctly and completely, in order to realise the performance gain from the correction. That may mean changing a couple more code segments.
If you have ANSI SQL, all the tasks are fairly straight-forward and easy.