I do notice the AI sometimes manoeuvring strangely, particularly if they sally from a settlement or if they bring reinforcements.

While they're going around your army, do you try to turn your army to keep facing their centre? If not, why not? If on the defensive you can usually redeploy much more quickly than the enemy can go around you. If need be, take your troops out of phalanx mode temporarily and make them run to the new position. This didn't happen historically, but neither did armies walk in circles around eachother on the battlefield.

Attacking with phalanxes works fine for me. The facing backwards thing is a guard-mode bug and also happens to my legionaries. You can fix it (as shown in this invaluable thread among many other things.) but it's annoying.

The right-click behind the lines thing works best for me when I'm attacking and the enemy line is being nicely immobile. I send my phalanx in first, keeping my other troops back to plug any gaps that might appear while attacking. I also pay close attention to stop the phalanx at the right moment, sometimes they keep walking too long.

When I have unengaged phalanx units I do not use them as legionaries, instead I draw them up behind/to the flank of the enemy facing the right direction via the right-click-drag method and then have them move forward "behind" the enemy to attack. Works fine, especially against outnumbered enemy phalanxes in siege-battles and such. The enemy gets stabbed to death from all sides.