I imagine your wife gave a statement immediately after and then in the cold light of day realised that she didn't want to take it any further?
Unfortunately, once your wife has made a report to the police of an assault and given a statement, it is out of her hands. It is not her decision to decide whether to prosecute or not and under the domestic violence protocols, the CPS are obliged to either prosecute (or the police have a discretion to issue a caution). So irrespective of what she thought about it, the CPS could (and would) still pursue it. Thus whatever you were told about your wife's willingness to go to court is in some ways irrelevant since the CPS could obtain a witness summons and witness warrant to get her to court and then apply to treat her as hostile. The only circumstances in which it would not pursue it is if your wife lied (and given what you have said above, this sounds unlikely).
I think in these circumstances, you are unlikely to be able to overturn a caution. There is the potential for an "abuse of process" argument, based on what you are told, but I do not know whether you can use this argument to overturn a caution (I only have experience of using it in court to quash proceedings).