I found a few "non-public" schools that are small and seem to have the right attitude towards immigrant kids, though there is not much proof of that other than the information on their websites.
Take it from someone with a significant amount of experience in such a school - they will pretend to care, but in reality, it will be a different story. I've seen how it works in reality - the kids struggling with Polish are often simply left to fend for themselves, perhaps with a token effort from a teacher to help them in Polish. How old are your kids?
I'm not sold on the private schools such as American or British, because from what I've seen on their websites, many of their teachers are not qualified teachers.
Couldn't agree more. I can tell you that a lot of them have teachers with thick English accents, the type that you absolutely wouldn't want your kids to pick up in any way. The very very best schools are comparable to a good public school in the Anglosphere, but that's about it. The stories I could tell about some of the more expensive ones...
My kids are in school all day (9:00 - 3:30) so having aupair does not make much sense financially at this point.
Could you perhaps take them out of school for a year while at home?
But - is there no Saturday Polish school where you are? They're all over Europe, but I have no idea if it's the same there. If not, maybe you could take a year out of work to establish such a school?