Yes, when you change the car ownership, it will be changed to the province that is listed as her address at the time, and where it is registered in her name.
To list it in Isaan you may need to drive it to Isaan, to do it in a DLT there.
It would be easier to do it in BKK. And keep the Bkk plates. It isn't a problem.
Better to do this things asap, in case there's something extra needed that the seller hasn't provided etc.
I'd meet the seller at the DLT in Bangkok as the point of sale. Hand over cash and sign over the name at the same time there. That way there's no hiccups or chance of dodgy stuff.