I'm really appalled the Accommodation Service did this, though not amazed. My experiences of them have always been crap, on both sides of the fence. Totally unprofessional, officious, and rude. They're apparently unaware that their entire raison d'etre is to HELP STUDENTS. Not threatening to evict them and their babies just before Christmas, snoop on them, or remove decent accommodation from the pool by annoying landlords beyond endurance. They treat landlords and students alike as delinquent adolescents in need of a firm hand - we won't go via them now, so appalling was our sole experience when we first wanted a lodger. If I really want passive-aggressive condescension, I'll be sure to contact them again. Luckily, our fab lodgers have always had friends eager to take their places, so it's never been an issue again. But if we do advertise in future it sure as hell won't be with them.
I'm sure your college have been fab, but as back-up, have you thought of contacting the Landlord & Tenant lecturer? I know it used to be an optional undergrad half paper (I studied law too), and the fellows are usually very good at helping students who are struggling with a legal problem, at least in my experience. Especially a single mother, I would hope!
Once this is resolved you also might consider lodging a complaint with the Uni committee overseeing the service, through your DoS or personal tutor. The AS have no grounds whatsoever to invade threaten to invade your privacy that way, legally or morally, and arbitrarily blackballing a single mother is beyond disgraceful. The idiots behind this royally deserve a smackdown from on high - after all, these idiots are paid by a university that's supposed to be there to teach and for reasearch; not to allow accommodation officers to go on power trips.