Launching a potentially decisive offensive usually involves an element of risk. The strategy employed by both Hooker and Lee at C'ville is an excellent example - pinning the enemy with part of your force while another part swings around his flank. There is inevitably a period during which your forces are divided. It's often pointed out how daring it was for Lee to divide his forces; it was daring for Hooker also, although not so dramatically. The solution, however, is not to waver at the crucial moment, but rather to press the attack home decisively.
As the Union flanking force advanced, they uncovered fords across the Rappahannock by which additional Union corps could join them. Pressing the attack brought them closer to reinforcements from the main body around Fredericksburg. The flank attack would actually get stronger as it advanced.