Exclude certain template from wp_list_pages

For children pages to show, the 'hierarchical' => 0 option must also be set in your get_pages() function.

I copied your code and initially had the same results (it returned no pages). Adding in the hierarchical setting set to 0 made it return the 2 pages I had set to that template, which could then be excluded. It then output all the other children except for those 2, as I think you wanted.

Credit for solution: Older Stack Overflow answer