I haven't read the whole thread so will probably repeat what others have said. The 4x4 joke is mildly witty but, for me, to laugh at it is to collude with a patriarchal way of thinking.
We all find life hard at times and have to make hard choices. We then seek to justify them to make ourselves feel secure and some people do this by slagging off people that have made different choices. Mumsnet has many examples of this, e.g. Breastfeeders feel smug and disapprove of formula feeders and formula feeders feel attacked and disapprove of judgmental breastfeeders.
Smug marrieds disapprove of single mothers because they think they are careless rather than just unlucky. Those who have lived a charmed life (thus far) look down on those whose lives appear haphazard but it's not as simple as that and religion has a lot to say about this.
Ok, maybe UJ is something other than just unlucky. Maybe she is not suited to long-term relationships. I think she is a bit bonkers, and possibly foolhardy, but, as some others have said, you do have to admire her resilience, ebullience and downright shiny, brazen, indefatigable optimism.
Why shouldn't she have children by different men? Matriarchal societies have been doing it for thousands of years. She is the constant in her children's lives and, although her career is not necessarily something to be admired, she does seem to be capable of financially supporting her own family. Stop the knee-jerk, brain-washed disapproval of situations which are different from your own or the prescribed norm.