Text alignment in text frames

I'm writing a song cycle, and the first page of the actual score allows me to center the title of the cycle and the subtitle (title of individual song), while simultaneously right-justifying "Words and music by [Joe Schmoe]." I want to repeat this at the beginning of each song, changing only the subtitle to reflect the individual song titles. My understanding is that this is to be done by inserting text frames in between songs. However, the text frames are not permitting multiple alignments; if I try to move "Words and music..." to the right, the title and subtitle move to the right as well. The same thing happens even if I put the title and subtitle in one text frame and add a second frame for "Words and music...". I suspect I'm missing something really simple, but whatever it is I'm still missing it. Thanks in advance.