This seems to be a power struggle. Even if you could accomplish it, your ex would probobly have the child poisoned against your wife by the time the child got there. Pretty difficult to deal with a child that is not your own acting up while the parents are away. Worse, the child could then say things that didn't happen and your wife would have no witness to counter what was being alleged.
I wouldn't put your wife in that situation of having to deal with your ex without you there.
I had a false assault charge pressed against me. It took me a year to get it dropped. If it would have stuck my life would have been changed forever. For instance, never again would I have been able to go on any of my children's field trips.
I know your wife is willing to do what ever it takes to help you, but think twice about the position you may be putting her into if you where to actually get what you ask for.