Also : make sure that you never sign any documents allowing the children to have a Polish passport.
I think that the original poster said that the kids have dual nationality but you're right, signatures of both parents are needed in order to obtain a Polish passport (even when the parents are divorced!).
Personally I wouldn't place too much faith in the US border guard and (as far as I know) they only keep lists of minors who are not allowed out of the country for 28 days. And I would place even less faith in the Polish family court. If he can get the kids to Poland, you may well have problems (possibly very severe problems) in getting them back.
I'd strongly suggest being pro-active: get a court order which specifically states that the children are never allowed out of the the USA without their mother and which requires that their passports are held by a third party. That way if the kids do have Polish passports, he will need to surrender them or he'll be in contempt of court. Also, if he does somehow get the kids to Poland, you won't be dealing with a custody case in the family court, you'd just be applying to have a foreign court order recognised by and enforced in Poland. Given his threats to take the kids to Poland and make sure you never see them again as well as you having sole custody and his threats to your daughter to have you put in prison, it shouldn't be too hard to get such an order.
As for his threats of legal action in Poland, nothing to worry about at all. But just to make sure, email citizen services at the US embassy in Warsaw and ask them to contact the public prosecutor in whichever city he'd report you (i.e. the one where he lives) to formally give him your correspondence address (and get them to ask to be copied on all correspondence).