Usually, irrational and illogical mean the same thing. Occasionally they do not. If you phrase the question as "What is rational but illogical?" or "What is logical but irrational?" it becomes clearer. I'll try to provide an example of each.
If you're willing to accept loving one's spouse as rational, it falls under "rational but illogical" since logic has very little to do with emotion. That's on slightly shaky ground, but that's a good segue for the next example. If you start from an irrational premise ("pleasure is sinful") you can come to a logical but irrational conclusion ("women who have orgasms are sinners").
I don't think spliting the parents is such a logical idea either. You double the probability that the children will suffer the loss of a parent. And the remaining parent will go through considereable suffering. Whereas the children will still experience considerable suffering and life disruption from the loss of even one parent.
If you're really concerned about all that, then line up foster parents before something happens.
I agree with the above in regards to irrational vs. illogical. Logic is old-school 'if A and B therefore C' type stuff.
But rationality implies taking a much wider view of the world. And doing what makes sense given the facts. And the drive to get enough facts to make a good decision.