Parent/Child relationship with custom records

I have 2 custom records, call them "Parent" and "Child".  I've successfully established the relationship between the two.  I can enter a Parent record, save it, then view or edit it and enter one or more Child records associated with it.  But, I do not like this edit-twice approach.  Is there any way to enter the Child records during the creation of a Parent record as a single-step process?

My real-world issue is that I'm trying to create a "Collateral request form" for employees to fill out to request printed materials from our production group.  I don't really want to flow these through the system as orders for security (and other) reasons.  So, I'm trying to build a custom construct for this.  The catch is that one person might request 20 or more different collaterals at a time on a single form and I'd rather not create 20 quantity fields and 20 collateral fields to facilitate this.