The landlord of the rented accommodation will need to do the TM30 for you, or give you the documents required to do it yourself at Immigration or registering the address on the TM30 website so you can do it yourself there.
But rented accomodation is fine for visa application and extensions, as long as you are staying there at the time of applying. Immigration might come visit you.
Yeah, I've done that now. I procrastinated it because I was super overwhelmed. Got some help with putting in the name of the owner and whatnot correct and it was smooth sailing. 😛
I will add here that whenever I've gone to Immigration ( Cha-Am, Petchabri ) to get this done personally, the Immigration officers wanted a recently dated confirmation from the landlord that they indeed was letting me do this process myself. I didn't have a recent letter, and they still did it, but they told me next time I would have to get a updated confirmation.
Wherever you are staying will need to file the TM30 for you.
Everytime you sleep somewhere else, you are supposed to get a TM30 filed.
Rented accommodation is fine for visa applications.
The last part I'm not clear on, but assuming it will technically be your wife who would need to do it. But you can make a account online for yourself and adding the address yourself there, with her owner documentation, and file it all yourself when needed.