Is there a way to rearrange home screens on iOS?
Depending on your setup, you have two options.


OPTION 1 - Use iTunes 12.6.3 instead. Refer to this answer for more details!
OPTION 2 - Use Apple Configurator 2. Download and install Apple Configurator.


Apple Configurator 2 provides much more advanced features in terms of managing your iOS devices. However, if you don't already have it installed, then the current version (v2.5) requires macOS Sierra 10.12.5 or later to run.

Once installed:


Connect your iPhone via USB to your Mac
Launch Apple Configurator 2
Select your iPhone
Go to Actions > Modify > Home Screen Layout...
Your screens will appear
Click and hold the mouse pointer on the screen outline and drag it to change its order. So, using your example, click and hold the outline for screen 3 and drag it to the left of screen 2.
Click on the blue Apply button at bottom right.