I know, AOG, and it does grate.
But as I suggested only yesterday, the root cause has to be tackled, not the poor old Home Secretary or the UKBA. And the root cause is the interpretation being placed upon the various bits of the Human Rights Act by the judiciary so I suggest you start posting in Judges' Weekly News or barrack the Attorney General about your complaints.
The children will, of course, have Britich citizenship, having been born here. So they can't be exported. Afterall you wouldn't like being exported whilst waving your British passport around, I assume?
It's a well-known ruse amongst those resdiding here and determined to stay - have a kid and your home and dry.