I may have found some birth and death dates for Paulinus Harvey Allred for you:
As for the Martin Willie Handcart companies since this wikipedia article for general info on all of the handcart companies including the 1856 company that your ancestor helped rescue. Leaving late in the season and caught by an early 68 members of the company had lost their lives. at least 145 members of the Martin, Mormon Handcart company lost their lives.
Here is the link to the Wikipedia article: http://en.wikipedia.org/wiki/Mormon_handcart_pioneers
A google search also turned up some additional info on your ancestor including a brief biographical history of him. It looks like he arrived in Utah in the 1847 Brigham Young pioneer company and then settled in Lehi, Utah.
Your ggfather and done of his sons are mentiond in the book "Pioneers and Prominent Men of Utah". Here is what the book contains on the two of them:
Allred, Paulinus Harvey
(son of Isaac Allred and Mary Calvert). Born January 21, 1829, Farmington, Bedford county, Tennessee. Came to Utah July 24, 1847, Brigham Young company.
# Married Melissa Norton (daughter of David and Elizabeth Norton), who was born in Indiana.
* James born January 10, 1849, married Kate M. Jones;
* Isaac H. born November 22, 1850, married Ursula Mulliner June 4, 1871;
* Dilbert born March 25, 1853, married Orinda Davis;
* Melissa born December 14, 1854, married Chris Peterson;
* Paulinus Heber born March 7, 1857. married Sarah Jacobs;
* Orissa born November 9, 1858, married Ed. Smith;
* Alma H. born March 31, 1861, married Luella Angel;
* Joseph H. born June 6, 1863, died child.
Family home Lehi, Utah.
Colonel Nauvoo Legion; seventy; assisted in bringing Immigrants to Utah.
Allred, Isaac H.
(son of Paulinus Harvey and Melissa Norton Allred). He was born November 22, 1850, Cottonwood, Salt Lake county, Utah.
# Married Ursula Mulliner June 4, 1871, Lehi, Utah (daughter of Samuel Mulliner, pioneer 1850, and Mary Richardson). She was born November 26, 1854, Salt Lake City.
* Paulinus Harvey born January 17, 1874, married Salome M. Kunz August 23, 1905;
* Joseph S. born June 1, 1878, married Mary J. Dayley February 26, 1906;
* Mary U. born February 12, 1880, married Ed. Parsons June 10, 1904;
* Sterling H. born October 3, 1882, died December 29, 1911;
* Lillian A. born October 1, 1885, married Robert Stone January 28, 1904;
* Fannie O. born October 6, 1888, married Herbert Adams January 9, 1912;
* Iona Rose born March 17, 1891, married Robert Manning July 24, 1907.
High priest; member first bishopric of Riverside, Bingham county, Idaho. Lieutenant of scouts during early Indian troubles.