Interestingly, the kids of the Pakistani men who have married non-Pakistani/non-Muslim women (that I know) are more influenced by the culture/practices of their mother and are more likely to associate with their mothers side. The kids don't practice Islam nor associate with Pakistani culture usually.
Well, first of all, the scholars have prohibited and most of them say this is not applicable to the western people and also not in non-Muslim majority countries where Muslim family laws are not implemented.
Secondly, that is the failure of those men. The vast majority of them married out of some necessity, either for the sake of citizenship/green card/permanent residency or some financial reasons etc.
Furthermore, 99.99% of such men are not practicing and they can mostly be a bad influence on their kids as far as Islam is concerned. I have spent all my life in the west and I know them...many of them drink, most of them rarely pray or tell their wives about Islam...so their children have nothing to associate with them and even less with their culture and religion.