Sliding should work in sub summary layout parts.
Two possible issues:
Are you in Browse Mode? Sliding is only visible in preview mode or when you print/save as PDF.
Is there space in the sub summary part above and below the slding layout object? That space won't be removed by the part resize, only the vertical space taken up by the empty sliding object will be removed by the resize--and then only if no other object in the layout part prevents this.