Upvote:2
The Schengen rules allow the German consulate to consider your application if you convince them that there is a good reason why you couldn't have applied for the visa in Indonesia instead.
One of the standard "good reasons" listed in the consular visa handbook (pp. 23-25) is if the need to travel to the Schengen area arose only after you left your home country and you can't reasonably be expected to travel back to make an application.
So there seems to be an excellent reason why you could get your application processed -- whether it will work in practice is hard to say and may depend on whether the consular worker who sees your application first has a bad day or not.
Your wife has less of a good reason, but there's a reasonable chance that you having a good reason might be enough.
Make as good an application as you can and hope for the best.