Of course they'll speak sufficient Polish by the time we move.
I wouldn't bet on it. There's a cliche in Polish education that children don't speak Polish properly until the age of 7 or so due to the grammatical complexity, but what should concern you is that they (as in Germany, I believe?) hit the ground running - they'll be expected to be able to read fairly complicated books by the time they reach 9 years old. So, even if your kids start at 7, they'll have a mountain to climb before they start.
Of course, it depends on their age - if they start a Polish language nursery at 2/3, they'll be fluent in Polish by the time they start school.
What should concern you most of all is that very little assistance is available for foreign kids that don't speak Polish. Polish classes are provided (2x lessons a week, only in the first year), but that's it. If you've got a kid that's 10 when he/she starts school, it's going to be an impossible mountain to climb, as there's no way they'll get enough from learning Polish as a foreigner abroad.
What are their ages? I can give you more specific and tailored advice if you tell me how old they'll be when you move there.
Is Szczecin the type of place that would be more accepting of a German kid starting school there?
It's likely to be the same level of acceptance throughout the country. Every class will have some kids where the parents listen to non-stop anti-German propaganda on public TV, and so there will be some issues.
You might want to consider something like this - gm20szczecin.edupage.org/ - where they will be much more accepting of other Europeans because of the name.