My family has owned land in TX since it was its own country, probably before, as far as we can tell. I never really thought about it until now, but the change from Mexican to American must have had some broader implications for the Spanish/Mexicans already living in the west of what is now the United States. But of course this goes much further than that, in the New World land was being bought up and sold by different countries constantly… but what about your average Joe? How did he deal with the drastic change in government?
I think that part of the answer is that during the period where large swaths of land were bought and sold, the power of most governments was pretty limited. Many landowners wouldn't have noticed much of a difference, other than perhaps a change in law enforcement procedures.
In areas where governments actually had significant power that affected landowners, I suspect the answer is the same as when the area of one country is conquered by another - landowners may not like the change, but they have no choice but to deal with it.