How can I sing high notes in my chest voice? (Bye Bye Birdy)?

I am Mrs. Peterson in Bye Bye Birdy and I am also an alto. I have to sing this song called, "A Mother Doesn't Matter Anymore," and my director says I have to sing it all in my chest voice. One of the higher notes is third-space C and whenever I try to belt it and sing it in my chest voice it goes flat. Any suggestions besides getting voice lessons?