@Mary *******
, where are you getting the information that the kids going to college on ED visas would need income statements?
As far as the mother you're confusing the requirements to get a Non-O-A visa from a thai consulate OUTSIDE the country with the requirements to get a Non-O visa (note there is no A after it) INSIDE the country at the immigration office, she wouldn't need a police back ground check or a medical certificate to apply for a 90 day Non-O visa.
The best advice I could give would be for ALL of them to get single entry tourist visas from a thai consulate before they wing their way here. That's because they'll get stamped in for 60 days and they could extend that by another 30 if they needed to at the immigration office for 1900baht. That 90 days would certainly buy them enough time to get their ducks in a row documentation wise so that the kids can apply for a 90 day ED visa and the mother can apply for a 90 day Non-O visa.