Lateral.
The word "laterally" means to the side.Lines that run side-by-side may be parallel.To place objects side-by-side is to juxtapose.
"Dextr-" is a word part that means right side. For example, "dextral" means pertaining to or located on the right side.
sway
Swiveled
The word is enate.
The word is 'through'.
Swaying and oscillating mean moving from side to side.
Sway
pinner
the butt
The root word 'lat' means side.
The word you are looking for is allies.