Some people are pointing out that they've successfully entered 7 times in a single year on a tourist visa or exemption and I have no doubt they are being truthful. However, if you are going to try to pull off something similar to what they have done, then I'd recommend you have a back-up destination plan ready to execute (e.g. Philippines, Cambodia, Vietnam etc.) Over the years I've seen numerous posts in this group and other groups, of people being denied entry because an immigration officer deemed that they were trying to live in TL longterm, on a tourist visa or exemption. Also and if you don't already know, you are technically required to have the cash equivalent of 20,000 Baht (currency from any country is fine) in your pocket, an onward ticket out of TL and proof of where you will be staying while in TL. Good luck, hope it all works out for you.
I'm going to assume that you got lucky while you were on your tourist visa and you were able to get a bank account without the need to go to several banks...correct? Well, you are not the norm. Time and time again I've seen posts in this group and in other groups where people talk about having been turned down at multiple banks, when trying to open an account on a tourist visa. Personally, I'd much rather drop ฿3K and know I'm going to walk away with an open account, than bounce from bank to bank to bank, hoping I might get an account but hey, that's just me.
Simple, use Bangkok Bank and pay an agent to do it for you, if you are on a tourist visa. If you're on a long-stay visa (e.g. OA, O, Elite, DTL, etc) then just go to the bank with your passport.
When I first went to extend my visa for the first time, I found the immigration document to be a little unclear so I did a Google search and I actually found examples of the form already filled in. Now I just keep a copy of last year's form and use it as my guide. That said, you may want to try a search if you're having problems.
Different immigration offices have different rules. Recommend you comment at which office you will apply, then maybe someone that uses that office can advise you.
Very difficult to get a visa and if you are successful, it will literally take months. Easier to fly her to Mexico and pay a coyote to sneak her across! Of course I'm not suggesting that you do this but it would be easier.
If it's not too inconvenient (e.g. a long drive for you) go to BKK bank and ask them in person. That way you'll know for sure what the bank will accept.