A validation rule controls what values you can enter.  It does not control whether you can enter it or not, which is what you need here.  To prevent user entry, one way is to disable the control on the form.  The control will be greyed out, thus preventing entry.  This needs to be done with VBA.  The code below enables or disables the [LoadComplete] checkbox field depending on whether the [PaperworkSubmitted] checkbox field is True or not:

Me!LoadComplete.Enabled = Me!PaperSubmitted

Put this line in the AfterUpdate event of [PaperSubmitted] and the Current event of the form.

You need some knowledge on VBA, the "event-driven" system used in VBA, and the purpose of events such as AfterUpdate and Current.  The other posters will hopefully point you to the right courses to take, if you don't have this knowledge already.

Here are the videos Kevin Yip was talking about:

AfterUpdate Event
On Current Event

Also watch: Intro to VBA

Thank you!

Is there also a way to do this between tables?  I can have up to 6 loads linked to a trip. I need a way to prevent a trip from being marked completed until all linked loads are also marked completed.

DLookup

I'm sorry Mr Rost, I don't follow you.  How does a DLookup work for this? Do I write the DLookup into the vba somehow?

Thank you again Kevin!  It works great on my load form!  Thank You Mr. Rost for the awesome classes and tech help videos!