I submitted [my daughter's] semester report form with her grades updated (credit for missed discussions from when we were [traveling], revisions for the [paper] in which she forgot her heading and parenthetical citation), but I do not see a way for me to update them on the website. Can you direct me? Or, if the Semester Report form has the correct grade, does the online gradebook not need correction?
There's no need to worry about updating the online gradebook display.
The Semester Report Form is your final authority on grades—those are the grades that will appear on [your daughter's] official transcript. The online gradebooks (both the ones you see during the semester and the final ones prepared by Miss Bethany at the end of the live classes) serve as helpful communication and tracking tools to help you calculate and monitor progress, but they don't determine the final transcript grades.
Here's the simple process: Use the online gradebook as your calculation tool, then confirm the final grades you want on the transcript by recording them on your Semester Report Form. Since you've already submitted [your daughter's] form with her updated grades (including credit for those missed discussions during your [travels] and the revision [of her] paper), you're all set!
The online gradebook will continue to show the original entries, but that's perfectly fine—your Semester Report Form has the accurate, final grades that matter for her transcript.