Hi Tanner,
Thank you for these further questions, as well as the explanation of what you are seeing along with the desired results.
I have set up my Approval User and Workflow to match what you included in your screen shots. I am getting similar results--up to a point. I'm my testing, SARAH creates the invoice and submits for approval. WHITT receives the notification email that the invoice "requires your approval". WHITT signs in and approves the invoice. This is where I have some different results.
When the Invoice was originally submitted by SARAH, opening the Approval Entries page for the Invoice actually showed three lines for this invoice. The first line was for SARAH which showed as approved. The next line was for WHITT which showed as Open until he approved, when the Status changed to Approved. The third line is for SHEILA and shows a status of Created until after WHITT approves--when it changes to Open.
Also, when WHITT approves, SHEILA does get an email stating that the invoice "requires your approval". This is different from what you were seeing. Here are questions that I have:
1. After SARAH submits the invoice for approval, have her click on the Approval button to open the Approval Entries page. How many rows are listed? Do they match what I mentioned above? I am guessing that you may have an entry for WHITT and not one for SHEILA--based on the fact that the record restriction is removed after WHITT approves.
2. If you have records in Approval Entries for both WHITT and SHEILA, then the approval by WHITT should drop you into the Workflow Step "An approval request is approved." with the Condition: "Pending Approvals: >0". Does this step in your workflow still look like this:

3. In order to ensure that WHITT and SHEILA received the email notifications, I did have to check the Notification Setup for each of the users. Do this by opening the Approval User Setup page and then for each user clicking on the Notification Setup. Ensure that you have records for both the New Record and Approval Notification Types. For both records, the Notification Method should be "Email", Schedule should be "Instantly", and Display Target should be "Web".
Based on my tests, it should be possible for both WHITT and then later SHEILA to get the notification emails that the invoice "requires your approval".
However, the last piece where you would like the original requester to get the email about the final approval is not possible at this time. The design of the workflow doesn't support this, although I completely understand where you are coming from. It is possible to have a specific (named) user notified of the approval, but not possible to select the "original requester". Here is an example of the approval step "An approval request is approved" with the Condition: "Pending Approvals: 0" where I send a notification to the TTORGERS user who is the equivalent of SARAH in your example:

Can you please log a suggestion on our ideas page to request functionality to add a Response that will "Create a notification for" the Sender ID or original requester? Here is the Ideas page: https://ideas.dynamics.com/ideas/dynamics-financials
Please let me know how this goes for you and if you are able to get closer to the desired outcome, even though sending to the original requester is not possible at this time.