I'm not a fan of mom doing all the work (and you know there are plenty out there who do the entire process on behalf of special snowflake), but like someone said above, when it's really important, all help is good. BUT, if Friend of Mom has been a lifelong friend and daughter has known FOM her whole life, she should make the contact. It's good practice. And in any case mom can make initial inquiries and daughter can follow up later to actually arrange an interview, send the resume, pics, etc.
Getting ready for rush, like planning a wedding, is definitely a team sport. But the daughter should be the quarterback.
In this particular case, our OP seems to be on top of it and is looking for a strategy. Fantastic. This tells me she's not expecting mommy to just handle it. If FOM in this case isn't someone you know particularly well, let mom take the lead. And also, I don't think you need to be terribly oblique about it. I mean, you don't want to walk up to strangers and ask if they're sorority women, but point blank asking your parents' friends, teachers, your adopted summer parents, etc. (people you know well) makes complete sense to me. They all know you going off to college is a big deal and that it's the epicenter of your life right now