Another tire question

op wrote:
I'm changing one of my tires on the back axle of my trailer because of cracking between the treads

Wise idea when one tire tread starts showing splits/cracks.

op wrote:
and got to wondering when you turn your trailer does it rotate on the front axle and drag the back axle

Sometimes.
However it depends on the terrain. If the terrain loads the rear axle tires the front axle tires do the sliding. Same with a nose high trailer on level terrain.
I've seen my tri axle trailers drag the center and rear axle tires.
And just the opposite if the terrain changes.