I had to give control to 2 of my other armies present on the field to the AI and it helped. The army under my control was fighting with one stack, while the AI went for another one. I was able to rout my enemy by separating their phalanxes from support troops, then engaging the support troops with 2 princeps, using my 2x classical hoplits and some princeps to stop their phalanx advancement from the front and moving everything else I had to outflank their phalangites.

In the end, after their pahalanx units were routed, I've split my forces to help those 2x princeps untits that were bravely holding against Parthian Spearmen Red Sea infantry and "Bnei Shevet Aravim", while other part of my army went to help the AI where some units were pinned down by the phalanxes of the second Ptolie army. Eventually I've won, it did cost me more soldiers than it would be if I could control all my armies myself, but at least I had a victory. And my 3-rd army didn't even have to enter field.

P.S. I've noticed that "Red Sea Light Infantry" says "Heavy Infantry" in their description on the battlefield. Why is that?

Second, turns out that Iberian Light Infantry are excellent phalangite killers. They've killed Klerouchoi even better than my princeps. They totally mess phalanx battle formation when attacking phalanx from the flank, something that my princeps units were unable to do. They've only forced phalangites to switch to swords on the flanks, but their overall formation remained intact.