Yes, the TTX program can handle your situation just fine. By registering for the sales tax permit and occupational license, that's what I meant (at a minimum) by registering your business in AZ. We just had a mild disconnect is all. Generally, for a sole proprietorship or single member LLC, one needs the occupational license at a minimum, issued in any and all jurisdictions where a business will operate. But so as to keep your federal taxes correct, you treat it as two separate businesses for tax purposes only, and that's it. That's because generally when operating in two states, tax agreements between states are in place (for many states) to avoid paying taxes on income twice - once to each state. Basically, you identify the "home state" for the business in each SCH C so that you only pay state taxes (and sales taxes) only to the state where the transaction occurs.
Be aware also that TTX does not "do" sales taxes. So you pay the sales tax to each state outside of the TTX program. At tax filing time, on both federal and state returns the program will ask you for state sales taxes paid, so you can deduct what you paid that state from the business's taxable income in that state.
I suspect you're aware of all this stuff. But perhaps others reading this thread in a similar situation may find it helpful. I for one am not familiar with CA tax law, and after attempting to understand it gave up.
