Sounds like government help did what it was intended to do
Your second lady, whose husband left and who eventually got a degree and a job, seems to have taken advantage of the programs and made herself a successful, independent economic agent who supports her children without further direct assistance. Sounds to me like a great justification for those programs. Too bad the hardship cases aren't all like her.
Your other lady doesn't sound as sweet, but if she's disabled and she worked before being laid low, then she's entitled to disability payments from Social Security. I assume the kids must be from a prior husband, since I don't believe they'd be entitled to support payments if she lived with their father. Is she actually married to husband #2?