You may want to consider redrafting your question. Your explanation has a lot of irrelevant details and opinions, and not a clear enough explanation of how the case has unfolded or what the courts have ruled and why.
It sounds like you're saying the court remanded as a result of a violation of the statute of limitations, but it's hard to understand why that would happen. If the original prosecution came after the SOL expired, I don't know how they expect to change that on remand.
In any event, an appeals court typically remands with instructions to do something specific. They may want the trial court to resentence a defendant, conduct a new trial, or maybe just dismiss the case.
The first option suggests that the court of appeals didn't find any reason to reject the guilty plea and simply wants to revisit the question of sentencing. In that case, a defendant would typically move to withdraw his plea. The rules and standards surrounding such motions can vary from one jurisdiction to the next.
The second option seems unlikely, as there doesn't appear to have been a trial the first time around. If this were the case, there would probably not be any need for a motion to vacate the conviction (a new trial means that the conviction was not valid) or withdraw the plea (a new trial necessarily implies a plea of not guilty).
The third option is obviously the most favorable for most defendants. If that's the case, there's probably nothing the defendant needs to do except sit back and wait for the trial judge to dismiss the case.
If I'm misreading the scenario and the remand has already resulted in a conviction, there's probably less that can be done to reopen the case, unless there's some amazing new evidence that was truly not available the first time around. In that case, though, there may be a possibility of seeking to have the conviction sealed or expunged. The relative triviality of the offense, the time passed, and the lack of any other criminal record suggest that this might be a good candidate for expungement.
In any event, anyone in this position should consult a lawyer to figure out what's actually going on and how best to proceed.