We agree about the million problems with Islamic culture & women.
But looking at the options, none of them are good. 1) Terminating the marriage...to what end? So the state can temporarily wash their hands? They'll be back together in less than two years even if you manage somehow to keep them apart in the meantime. But at the risk of creating criminals and lots of problems. 2) Ripping the kid away from the mother...very cruel, doesn't solve anything, creates an orphan and an incredibly hurt and pissed off couple of people. No benefit to society, all downside. 3) Deporting them and really washing their hands of it, but why let them come in the first place? A refugee brings their problems- if you don't want them, don't accept them. And why condemn them to Syria? That's just creating a tragic 3 act play. So much for statecraft. Or, 4) Keep an eye on them and provide for the child. You reserve options 2 & 3 this way, and you give the situation a chance to play out as it would, rather than stepping in preemptively for no gain.
Clearly the time to address this is before they are accepted into the country.