We will be in Poznan for at least 4 years, so would like to make a good chocie of schools for them.
Alas, your options are rather limited. Both international schools here are expensive and are of shockingly low quality, while the Polish education system is likely to be a rather big shock for them as the culture is completely and totally different.
My only suggestion would be to try and get them into one of the so-called social schools - but there aren't many of them and they're very popular.
I'm sorry to say that it's likely to be a huge struggle for you if you can't afford to put them into private English speaking schools. While the 9 year old might cope (and even then, I have my doubts) - the 11 year old is definitely going to struggle in the Polish middle (secondary) school as they simply won't make any allowances for her in the public schooling system.
Homeschooling is also much more difficult in Poland than elsewhere - there are many checks made and an approved programme must be followed.
If I can be of any help at all, give me a shout.
I've been thinking about this some more, and I simply cannot see how you can make this work on any practical level. However, if you're determined to go ahead with this, then -
1. You'll need to spend a year "integrating" them into Polish society. That means intensive Polish classes (4-5 hours a day) combined with many extracurricular activities where they integrate with Polish children. You could get a Polish teacher full time for around 2500-3000PLN a month for someone capable enough to bring them up to standard. This also will place huge stress upon your children - Polish schools simply will not accept "me no speak Polski".
2. They'll also have to spend considerable time adjusting to the Polish system of learning facts - which is totally different to the British model of applying knowledge. This is going to be ridiculously stressful for them.
I'm sorry to be the bearer of bad news, but Poland really isn't very well set up for non-Polish children attending State schools. The class sizes, the programme - Poland very much follows the "classical" system of education.
As for the two private schools - you'll be looking at somewhere in the region of 15k PLN a year each for them.