One option may be to use a unique identifier, like the instance ID of the original process/submission, then create a second form for your supplemental documents that has a hidden field for that identifier.

In your first process, when additional documents are required your process could trigger an email that contains a URL that will prepopulate that ID on the second form.

When the second form is submitted, you can then use the identifier as a metadata field to find and merge the documents, or something along those lines.

As an example, a public user submits a form and starts instance 12345, the employee indicates additional terms must be accepted. They click a button in the Form 1 process, which can automatically email the public user with the following link using the process variables

https://yourdomain.com/forms/form2?id=12345

The users opens the link, which prepopulates the "id" variable with 12345. When they submit the form, you now have a way to connect the dots between form 1 and form 2.

Obviously there's a lot more to figure out, and I don't know enough about your process to know what approach is best, but this should give you a general idea for how to establish that link between the two submissions.

I dealt with something similar not too long ago.

I would populate a separate table in a database (not the Forms database) with the data from the rental request. Include a unique "rental request ID", etc. and inform the user that the number is important! As it is reviewed and determined that additional agreement to terms & conditions is needed, have Forms kick off a workflow that inserts that data into your table. That is how you can tell if the email you mentioned gets sent out. 

Have a scheduled workflow run every X days to retrieve all active records from the table that need the email sent. Email the user with an email address (a required field on your rental form). Have a separate Forms process altogether that the user must enter their unique ID into. Once entered, do a lookup to populate the form with data from your table. Once the agreement of terms & conditions has been submitted by the user, have Forms kick off another workflow to update your table indicating the second agreement has been received. So in other words, use the table to track the data and use multiple forms to write to it.  

Good luck, you got this!