Because of what I have read about Peter Meinke's life, it seems more likely that this is an imaginary poem that the poet's father may have written, when he was sober enough, to his ten-year-old son, now the poet.
Peter Meinke had four children: three boys and a girl. One of the children was, indeed, named Peter, but I don't think he was the eldest. Besides, from all I can ascertain, Peter Meinke, the poet, had a stable life and a happy marriage and now has a number of loving grandchildren. There just doesn't seem to be room in his life story for the rage and callousness that is evident in the poem.
Here's a hint, from Peter Meinke's poetry book called Scars, that may help settle the matter:
When I was young I longed for scars
like my father’s
They were the best
scars on the block
pink as a tongue against his whiskey skin