I'm so thrilled someone else noticed this music, too! (I tried adding it a while back to imdb's soundtrack listings for this movie, but didn't succeed). anyway, the piece you hear used throughout mamma roma is the second movement (largo) of vivaldi's piccolo (flautino) concerto for piccolo (or recorder/flute), strings & continuo in c major (RV443) [allegro-largo-allegro molto]. it's a sopranino recorder you hear in pasolini's movie; I don't know what recording he used.
it's beautifully haunting.
you can hear a version of it on youtube here [at 4:02]:
but to my mind the best performances of this on recorder are by marion verbruggen (on sopranino recorder) and dan lauren (on voice flute, which is an alto recorder that's been tuned a third lower, in d). to my ears, verbruggen's version on sopranino has an etherial, unearthly quality; laurin's has an earthier, plaintive quality.