We do it all the time. The airlines usually know this and may ask to see both passports, especially when the stay is longer than 30 days (visa exempt) when you present only the US Passport.
Once she gets her USPassport, she should use her US Passport to exit America, then use her Thai passport to enter Thailand, then use her Thai Passport to exit Thailand and finally use her U.S. Passport to enter America. This avoids any need for any VISAS. Good luck.
everything is done online. Once approved, your consulate that services your paperwork emails you the visa paperwork which you present to immigration in Thailand with your boarding pass.
Your question: “Is there a way to keep my American number without paying $45 a month?” - unfortunately once you cancel service, you will loose that number. But - read here:
Yes and one of their locations is at the Trendy Building located on Sukhumvit Soi 13 with easy access to both the BTS Nana Station or MRT Sukhumvit Station not far from Terminal 21.