the takeover of BD mainline by BA at the currently agreed price was on the condition that LH sold the Baby division, and that a significant price reduction would be in order if a buyer could not be found?

The takeover of BD mainline by IAG, but otherwise correct.

if BA/IAG is forced to take on the Baby division, would they perhaps look to hive it off to BE

Although BA does own 15% of BE it is a silent partner so has no say in BE’s affairs and I really don’t see BE wanting WW. I think it more likely IAG would look to offload WW to LS (the fit would be better for LS than BE) for a nominal fee. If that doesn’t work then I fear WW will be history.