After all it's not that difficult for her kid to get a polish passport
For sure it is not but the time frame he is talking about might not be ideal for him.
In Warsaw you'll need to find an office that is not very busy.
September is quite a busy month for civil marriages but your partner can ask around to find an earlier date.
If she finds someone understanding I'm sure you can get married during your 2 week holiday.
All the best.