"No. You don't." Because no one did, not really. That was what made him dangerous. But Bruce could satisfy himself that Hal at least knew enough to understand the seriousness of what they were facing in that one piece of the threat against them. Bruce doubted the full weight would come down on them, but it was at Ra's disposal, and he wasn't taking any chances.
Hal's assurance was not surprising, and at any other time, given the circumstances, Batman would have taken him at word value, even if he wouldn't admit it. Batman understood Hal's devotion to Dinah, the strength of their friendship, because he felt it, too - not just for her, but for others with whom he held the same incredibly tight bond that pair shared. While he did believe Hal was confident in his abilities, and Batman wanted to believe that was enough - it simply wasn't.
Did he really think Hal could be distracted by Talia? "Yes." It was as simple as that. Dinah or no Dinah, all it took was one minute, one second. "I just told you Damian is hers. You don't get details." But whatever else Hal might think of Batman, he was not known for his lack of self-control. He was also overly-cautious.
"I trust that you will do everything in your power to protect Dinah," Batman allowed, walking toward the roof's ledge to scan the surrounding architecture, their distance, and the streets below. "As will I. All I ask is that you never make the mistake of underestimating them, or thinking you know them. They already know you better."