What exactly is it that leads you to the conclusion this lady is an illegal alien? In the article it says she came here to visit her mother-in-law. She's probably here on a visa. It's not like we have a border with Sudan where this woman could have snuck in. She probably came in on a plane with her passport and visa in hand.
“What are the odds these kids will be on welfare (100% or 100%)?”
What makes you so certain these kids will stay here? The mother was just here visiting. She wouldn't have an immigrant visa if she is just here visiting. Her kids might be considered citizens because they were born here, but they can't file paperwork for an immigrant visa for their mother until they turn 21. Chances are she'll go home to her husband and take the kids with her.
Odds on leaving with 5 children that are US citizens, unless a diplomat, 0%.