My daughter-in-law lives with her husband in America with "green" card status.
She wants to become a U.S citizen, but is afraid she will lose her Thai property ownership rights. She currently owns a fair amount of land in Thailand.
Does she lose her property rights?
Does she lose her ability to visit Thailand as a "Thai" and have to use non-resident visa rules for entry and visitation?
Does this affect the nationality/rights of her Thai, native born minor sons as to their inheritance of her real property?
Thanks for your consideration.

Thailand recognizes duel citizenship. She would lose property rights and or other if she renounces her Thai Nationality. As for travel, she would leave USA on US passport and enter Thailand on Thai passport, have to show both upon entry. And it shouldn't have any effect on her Thai born children. Google "Thai Nationality Act" for more info (Chapter 2, sect 13).

No problem, my sister in law has Belgiun citizenship and owns plenty of land and a house in Udon.

Same here, no problem. My wife is USA and Thai citizen. Shows only Thai passport when entering Thailand and US passport when entering US. We returned to Thailand last April and she only showed Thai passport to enter.

There used to be a law that disallowed land ownership for persons married to foreigners. That law was changed in 1999, I believe. My wife recently bought land and has owned land and a building here for a long time.