there's a FAQ on Wise about Thai baht transfers that tells you what you need to do if it's important to prove an international transfer. Even Wise recommend using SWIFT if it showing as an international transfer in your thai bank is important
They may want to see proof of how you can support yourself for the period of the visa but its probably best not to give that up front and wait for them to ask if they want to see it
Assuming you enter under the visa exempt rules you get stamped in for 60 days and can get one 30 day extension from your local immigration office and then you must leave. You can try repeating this but whether or not you are allowed to enter again will be up to the immigration officer you will stand in front of
Be wary of doing this on the account you use for your extension of stay. Even assuming your immigration office will accept joint accounts you would need double the money in the bank as they view only half the money belongs to you. Get her an account of her own
best thing you could do is leave Thailand without a re-entry permit, apply for a fresh Non-O visa using your own funds then do the 12 month extension by meeting the criteria of the immigration office that serves the area where you live