What was the biggest factor in leading to spain having problems controlling new mexico and texas?

Part of the problem was the resistance of the indigenous peoples like the Apache to the Spanish control and then later to the Republican Army of the North of indigenous people and Americans who harassed the Spaniards and made them relinquish the territories.

Texas decided to separate from Mexico, when US immigrants decided to start a war of independence, which is also supported by the USA. As the most important reasons, the fact that since the colonial era, Americans began to arrive in Texas to live, eventually married people of Mexican origin, but they did not feel part of the country, and when there came a time when the population of Americans was much greater than that of Mexicans, in that situation they agreed to separate from Mexico and request their annex to the United States, which caused the Texas war and its annex to the USA in 1845.