The Non O from USA will give her 3 months, then she must get an annual extension which requires cash in bank for first one. You can only use income for subsequent ones. However, if she gets a Non O-A in the USA it will give her a year, but it does require health insurance, criminal check, medical form etc. You would have to wait until she was 50 so would probably need to delay the trip.
Apparently, I was wrong about your brother. I apologise I always thought it was 18 not 20.
Unless you and your brother are both willing to buy an Elite visa there isn’t really any visa that suits, at least not easily. An Education Visa might be a possibility if either are willing to register for an appropriate course, but they are looked at with suspicion by Immigration due to frequent abuse. Another option is to try and get a job with a company that will sponsor you. Otherwise, you’ll need to get Tourist Visas and leave the country periodically hoping g that immigration don’t flag you.
It would be much easier for your mother to get a Non O and she can then stay permanently. This can be got in your own country if you wait until she’s 50 or can also be got inside Thailand if she enters on a Tourist Visa and is 50 when she tries to convert it. She will need
*****
0 baht in a Thai bank account to do it herself, unless she’s willing to use an agent to help. Your brother is 18 so can’t go on her visa.
A friend and his wife has done it for about 4 years now so I guess he’ll be grandfathered in. He meets all financial requirements etc but uses an agent for convenience. There might be a chance of an agent still to be able to do it, if no other way is possible?? Otherwise, the OP is stuck really, other than paying for Elite.
Thai Airways probably the most reliable, followed by Bangkok Airways. No guarantees but generally better than the budget airlines. Also, both fly from Suvarnabhumi so you avoid Don Mueang.