Is this realistic?
Yes. The dramatic performance plays out in the same way that it would in the U.S. Court system.
The actual killing of the wife would be 'legal', so can he be charged
for murder for something that has been done legally, only because they
can prove is intent to kill her before that? Especially since he has
already been acquitted of that fact.
Mostly, this is an issue of causation and not double jeopardy.
From a double jeopardy perspective, the crime of murder is not complete until the person dies, and they have not be tried for murder, so this is a different crime that had not occurred until after the attempted murder trial was over.
Even if the immediate cause of the wife's death is withdrawal of life support, the shooting could still be a legally sufficient cause of the wife's death.
For example, suppose that you shoot someone and the hospital can't give the victim a blood transfusion because the victim has blood type O- (universal donor) which can only receive blood from other people with blood type O-, and the hospital, due to negligence on the part of a hospital administrator, has run out out of type O- blood. The fact that the victim would not have died if the hospital has not negligently failed to have type O- blood on hand does not provide a defense to murder on the part of the person who shot her.
While terminating life support is "legal" it also constitutes a non-judicial finding with legal effect on the part of the person authorizing it and the physicians signing off on the decision, the further medical care would have been futile and that the person whose life support was terminated was already dead in key material respects, even though they would not be dead for purposes of a murder charge until life support is terminated.
When death is a natural and foreseeable result of action that causes physical harm, the death is caused by the act that causes the physical harm. Something else that causes death would have to be a "superseding cause" and not just an additional cause of death.
Thus, the fact that life support was terminated legally does not mean that she cannot be a murder victim. Indeed, many murder victims are people who are on life support for some period of time and then have that life support terminated because it is futile to continue medical care and the person is already "brain dead" or something equivalent to that.
Collateral Estoppel Issues
Double jeopardy does carry with it a related concept of "collateral estoppel" which provides that facts necessarily decided in one criminal case cannot be decided differently in a subsequent, related criminal case in some circumstances. But, collateral estoppel applies only when the facts in the prior criminal case were necessarily decided on the merits in the prior criminal case.
Acquittal of criminal charged does not necessarily include a determination that someone was innocent of the charges. The fact that he was acquitted of attempted murder does not mean that the jury found that he didn't attempt or intend to murder her.
In particular, a dismissal of criminal charges as a result of a technicality that excluded evidence related to an element of the crime for which there was an acquittal, is not a determination on the merits that a particular element of a crime was actually absent, so it would not be binding in the subsequent criminal case for murder. An acquittal does not mean that every element of the prior criminal charges was found not to be present.
Collateral estoppel arising from the double jeopardy right, in contrast, might be a ground for dismissal of the murder case, if the man's primary (and perhaps only) defense to the attempted murder case had been that he had established the affirmative defense that someone else committed the murder, or that he had an alibi that made it impossible for him to have committed the murder. Then, the jury would have found on the merits that this defense, equally applicable to the murder case, had already been established.