How to toggle custom WP archive list

I know nothing about the theme or plugins you are using.

Since your theme isn’t responsive you could get away with the down and dirty approach if you can edit CSS files:

/wp-content/themes/mytable/style.css line 262
.content-bar {
  border-right: none;
  width: 890px;
}

/wp-content/themes/mytable/style.css line 181
.right-sidebar {
  display: none;
}

Or override by adding your own CSS file.

If @majick’s solution is an option that is far better than this answer.