Final answer:
Sam Houston resolved unrest in the Texas army by leading a surprise victory at the Battle of San Jacinto, capturing Santa Anna, and subsequently signing treaties to end hostilities. Houston's leadership as the president of the Lone Star Republic, and liaising with foreign nations further stabilized Texas.
Step-by-step explanation:
After the Texas Revolution, Sam Houston faced the challenge of unrest in the Texas army. Houston, who had gained considerable respect as a military leader, was able to restore order by leading his troops to a decisive victory over Santa Anna at the Battle of San Jacinto. This battle saw the Mexican forces taken by surprise and quickly defeated, which significantly boosted the morale and unity of the Texan forces. The subsequent capture of Santa Anna and his signing of the Treaties of Velasco also helped to pacify the army by providing a sense that their struggle had achieved a tangible result, namely the cessation of hostilities and, though tentatively, the recognition of Texan independence.
As the first president of the Lone Star Republic, Houston continued to lead Texas with political skill by managing the fragile new nation's domestic and foreign affairs. His leadership helped to steer Texas through a turbulent period until it became an official U.S state in 1845. Houston's ability to inspire his soldiers and his strategic acumen were crucial in solving the unrest in the Texas army.
With his presidency, Houston further stabilized the region by enticing thousands of American immigrants with promises of land, which increased the population and strength of Texas, although it also led to political tensions over the possible annexation of Texas into the United States and concerns over the slavery issue.