Cocklin - Millard

I'm looking for information on Peter Cocklin born abt. 1831 in Pennsylvania. I have found him on the 1870 U.S. Federal Census with a wife, Lavina, and children: Daniel (18), Elizabeth (15), John (10) and Aldavine (7).

Again, I found him in the 1880 census in Harrisburg, PA, with wife, Lavina, and children: George B (23) and Alda (16).

I found a Peter Cocklin in the 1860 census in Pottawattamie, Iowa. He seems to be the correct age of the Peter I am looking for, but his wife is listed as Francis A (born in England), children: William J. (9), Anna J. (7), Elizabeth (5), and Caroline (1). All children listed as being born in Pennsylvania, except for Caroline.

The person in my tree is Mary E. Cocklin Millard, born Aug. 25, 1854 in Sherherdstown, PA. Peter & Lovina are her parents. I'm wondering if Elizabeth in the census, is really Mary E (E possibly standing for Elizabeth). The ages seem to be correct.

I'm also wondering if Peter was married twice, first to Francis and then Lavina? And how all the children figure in.