Protected Page-Want widget to appear only on the second page of a protected page

I am using the Coraline Theme and am using a protected page on a portion of my website. On the first page of the protected page you are required to enter a password and once you do it takes you to the second part (page) of the protected page. I am using a widget that I only want to appear on the second part of that protected page and not on the first part where you enter the password. Since both of these have the same page title/name I just can’t figure out how to do this. It can’t be done on the widget page because if I say to display or not, it does it on both pages.

I am hoping someone can help me but maybe it just can’t be done.

Thank you.