For the history of the San Patricio Batallion, the University of Texas has the "Handbook of Texas" Online at San Patricios which should take you to the article on the Patricios.
I will extract a few lines.
"By the 1840s a significant proportion of the enlisted men in the United States Army were Catholic immigrants from Ireland and [what is now] Germany. The Mexican government started a campaign after the Mexican War broke out to win the foreigners and Catholics to its cause." Mexican propaganda insinuated that the United States intended to destroy Catholicism in Mexico...." In Nov. 1846 Gen. Antonio Lopez de Santa Anna organized American deserters with other foreigners in Mexico to form the San Patricio Batallion, a name it probably received from its Irish-American leader, John Riley [?often mis-spelled Reilly; US rolls said Riley] formerly a member of Company K of the Fifth United States Infantry."
"The Company saw action at Monterey, ...Saltillo..., Buena Vista and at the battle of Churubusco in August 1847." "As American forces rapidly approached Mexico City....Santa Anna decided to concentrate his forces at Churubusco where there was a fortified bridgehead...." He stationed the San Patricio companies with a battery of five cannons on the bridge..." [skipping the lost battle]
Those captured "did not fare well." Gen. Winfield Scott issued "General Orders 259 and 2263 establishing two courts martial for the 72 deserters (one convened by an Irish-Catholic officer, Col. Bennett Riley). Scott....gave 20 the death sentence. "John Riley, the leader, technically deserted before the war...was declared, so he could not be hanged. He received fifty lashes and the letter "D" branded on his cheek." From the other courts martial, Scott confirmed the death sentence for thirty. Those from the first trial were executed at Mixcoac. "the latter sentences were carried out under the command of Col. William S. Harney, who had the condemmed men fitted with nooses at daybreak and then left them standing on the gallows while the battle for Chapultepec Castle raged nearby." The men were hanged when the Castle was taken.
By March 1848, Mexico had found enough original San Patricios and new deserters to form two more companies.
After the War, the San Patricios continued as a group, patrolling areas of Mexico to protect the people from bandits and Indians. The unit was dissolved late in 1848.
While some members of the San Patricios petitioned the government of Mexico for help in returning to their European homelands, most remained in Mexico because they could not return to the United States.
Estimates place the number of Irish-American deserters at 40-60% of the San Patricio Batallion. The remainder were other foreigners and Mexican citizens, some of these Irish.
Mexico lost 870,000 square miles of territory to the Americans.