Ok first off Penguin only confronted Batman in front of Schreck's because he was now a mayoral candidate, and now the "Political" thugs had his back. Batman new better than to take a chance at that moment, because he could be set up again, for attacking a political figure. Catwoman was the intriguing villain in that movie, because she was so low-tech.
Since Catwoman was a self made villain, she had the right to intervene at will between Batman and Penguin. I liked that because she got her revenge on the person she resented the most, no "real" sub-plot for her minus the quasi love quadangle (real word? You be the judge) between her two personalities and Batman and Bruce Wayne.
As far as Penguin being alone when he framed Batman, be careful how you phrase that: He was never alone. During the kidnapping frame up and planting of the Batarang, he was assisted by the poodle lady. During the killing of the Ice Princess frame up, he was already protected by the political powers that be (Max Schreck and his political commitee). Penguin knew that being in any particular place with Batman alone would be a bad move he would of had himself covered.
Before you say he was by himself on that roof when he threw that umbrella, full of bats, remember he is now a political pawn of Schreck, and he will have an alibi after alibi to cover up Penguin's activities. With this kind of "immunity": Penguin can pretty much do what he wants. Just look at his converted campaign/Batmobile command center. Even though that van was rockin' no one came knocking. Bottom line: Penguin performs better when he has insurance of his own protection, be it thugs or the law.