Given that it is one set of facts to justify the infractions alleged to be committed and the elements of each violation are inherent in each other, your argument makes perfect sense, so although she may be found to have committed both acts, punishment of both infractions would in essence punish the same act twice.
Why do you think that these violations are the same? They can each be committed separately, but your wife happened to commit both of them at the same time because she didn't want to get wet or have your kid get wet so she didn't care about blocking others AT AN ELEMENTARY SCHOOL with her car. That's why your wife got 2 tickets, because she was at a place where extra care was supposed to be spent, and she instead ignored 2 basic parking laws.
The fact that she left her car for only 40 seconds and the fact that it was raining are excuses that don't appear anywhere in the Vehicle Code, so you shouldn't have expected to win any appeal over such blatant, if brief, violations of the law, especially near a place where EVERYONE is worried about their kid and NO ONE wants their car blocked by someone else.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
It sounds like Parking Enforcement felt pretty strongly about the offenses to warrant busting out the video camera. If you feel strongly about it, speak to a lawyer. A more thorough response would require an evaluation of the specific offenses on the citation. The government is up to all kinds of tricks to try to raise revenue these days. But issuing video cameras to parking enforcement officers? Sounds like a bit much. But yes, You can in fact be charged with 2 separate charges if the facts fit.