Modify new child page layout when triggered by parent page

In my app, we have a list of companies in one data set, and contacts in another. Our user can clic "Add business" which launches that form, and the contact field allows the user to add a new record. That launches the default layout for adding a contact, which has a bunch of fields I do not want the user to see. However, there is currently no way to modify these child pages. That would be a huge help!