Shopping cart delete button is not removing the correct line item.
Sounds to me like both of your forms on the page have the same form ID and use the same numeric key (likely 0) to identify the first item in the form. Thus when you submit it, Drupal doesn't know how to differentiate which form was submitted and makes a best guess, removing the 0th item in that form.

Alternately, if your configuration is generating a form within a form, that's invalid HTML and would explain a similar confusion on Drupal's part for the processing of the form. You would need to find an alternate method for getting the secondary form on the page, such as using the block system to embed the second form on the page.