Please post card links/scans in the future when posting questions here.
I understand what you're getting at, and Politoed LA's "Enthusiasm" Poké-BODY does not work that way. Once Poliwag is evolved into Poliwhirl, it is considered Poliwhirl (no longer Poliwag). You cannot evolve a single Poliwag ---> Poliwhirl ---> Poliwrath and have Politoed's BODY kick in. You need to have - separately and in play - a Poliwag, a Poliwhirl, and a Poliwrath taking up 3 different spots on the playing field.