dude has never shown a single interest in his kids now he's going to head into the viper's nest to 'steal' a girl who he can't admit is his daughter and is engaged to the heir of Dorne?

Bronn's ambitions were to be lord and he was there. Does dude really strike you as the type to care that his wife's a bit off? And he'll just put that aside for a secret agent mission about realm matters he really gives no shit about?

There's no reason for it to even be secret. Send a 'diplomatic' envoy and then steal her back. It's just overly complex in a time when they are trying to over-simplify all other plots.