I have created an employee contract to be filled in on line by Owner with a portion that the employee will sign and email back.

How does this work? If owner of the company uses the direct link to the form to fill in the contract that she will email to the employee for a signature of acceptance of the position.

I did add a submission Button. Does she fill out and print and do the email with printed copy with instructions to the employee to email back to company.

The submit is suppose to clear the form. 

It is possible to fill a form by 2 respondents. I would suggest to apply conditional logic to send an email containing edit submission link to employee for signature. Another condition can email back the form to owner. 

Please review the following articles for more information. If you encounter any problem, we will be glad to assist.

How-to-Let-Users-Update-Their-Form-Submissions-at-a-Later-Date

How-to-Send-Email-Based-on-User-s-Answer

A-General-Approach-on-Building-an-Approval-Process-Workflow