One might find a very different West Coast. I think you could avoid the war with Mexico by having the Texans accept the British proposals for guarantees on their independence in exchange for relinquishing claims on modern New MExico, maybe with a boundary at the Nueces - Pecos rivers in the South and the Red River in the north with the northernmost claims bought out. I suspect the Mormons will seek to purchase territory or at least rights of occupation/settlement including modern Utah, western Colorado along the lines of the Mexican claim, south to the Arizona river, and west to some undetermined point - maybe a near-approximation of modern Nevada and eastern California? With the discovery of gold in Northern California there will be an influx of foreign and especially American settlement, Washington will be eager to control the area for at least everything north of Monterrey, leaving the Central Valley to the Mormons or Mexico. If Mexico decides it needs money in a hurry they might do a deal with Texas or the Mormons as the riches of California would exceed the potential rewards for either alternate location.
The American Civil War would likely be avoided but as time passed the Texans would perhaps keep slavery alive, leading to an emigration from the United States should the practice be outlawed there probably about 1870 (+/-5 years). Money and workers will come into Texas while the cattle industry will develop. I could also see Louisiana and Arkansas politicians discussing secession to join Texas but this would not likely pass. What might work is a wealthier Texas offering to buy the Indian Territory from the United States for a nice sum, expanding the fledgling Republic. If Mexico falters on her debts as per OTL about 1862 and is still struggling with the prospects of what to do with Mormons in Utah, Texas as a whole, and any number of affairs in California, then the entirety of southern North America will look very different by 1870.
One possible scenario in 1870:
An independent California inclusive of much of her OTL borders save the easternmost part of the state down to about 35 degrees north latitude is prospering. It is a UK-backed government out of San Francisco whose gold seems to disproportionately end up in London while Washington has a great deal of influence as well. There is a Mormon theocratic Republic of Deseret running from the eastern edge of the Sierra Nevada to the Colorado River and along the San Juan river covering much of what is OTL western and southern Colorado. Texas is an independent republic that bought the Republic of Mexico's claim to everything east of the Rio Grande at her nadir with Maximillian's Empire and follows that river as its boundary to the Gulf of Mexico. Austin makes no secret of its hunger for even more land and seems to have her eye on every Mexican state on her southern border along with Sonora, Chihuahua, Baja California, the leftovers of Alta California, and even Sinaloa and Durango. Her newfound wealth from cattle and cotton via significant immigration from the Southern United States triggered an economic depression there when the 1868 Lincoln Amendment to the Constitution was passed. Texas has also made overtures to purchase the Indian Territory and is in negotiations with the United States who seem quite amenable to its transfer.
Mormons are weary of outsiders but perimt their passage through the Republic of Deseret in exchange for a toll along the California Trail. With the United States feverishly building a railroad from Independence MO to Portland Oregon expected to be finished no later than 1872, Salt Lake City officials have wisely begun building their own from the border town of Denver, RoD to a new community at Lake Tahoe known as Youngstown. With European immigration to all of the above increasing and Texas eyeing land on the Pacific Ocean, there is little central government in the border areas to say what law there are or are not. With the very recent conclusion of the Civil War in Mexico in favor of Juarez, who may now seek to consolidate power from the semi-feudal and semi-independent governors in the northern states/territories, anything is possible. The departure of Empress Carlotta and her now 2-year-old son Augustin also means that there is a blood heir to the throne of Mexico. Despite Maximillian's execution he might return someday to claim his place as leader of Mexico as he is very safe in Belgium under the eyes of a very protective grandfather.