Where did family breakup come in to it?
It doesn't really matter if there was or wasn't a break up. The point is that it's a parent of three children trying to do it on their own, which is ten times harder than if there are two.
Having said that, if the individual in the story cannot afford the mortgage now and needed benefit help to make ends meet, then it's highly unlikely her ownership of the house is anything other than the result of a break up with her partner/husband.
The cost of (good quality) childcare is pretty scary. Full time child minder is in the order of £700 to £1000 per month. Nursery fees aren't far off.
I still don't think that the story is highlighting the cost of childcare though; it's highlighting the cost of being a single parent, both to the parent(s) and the state.
I also don't think you can argue with the notion that we have made it terribly easy for people to be in this situation.
First you make marriage less of a big deal
Then you make divorce easier to grant legally speaking
Then society decides it's perfectly OK for people to get divorced
And then society becomes increasingly fickle and self centred thus accelerating the situation.
And before you know it you've got a several hundred? thousand? percent increase in the number of single parent families trying to make ends meet on one income (i.e. maintenance) spread across two households.