Will I have problems getting hired again if the business fails? Will
this be a huge stain on my resume? Would it say that I might have a
problem with authority?
It might cause problems, but it might not.
Having a business fail isn't usually the problem. Switching from being an employee to a business owner and back to an employee again is usually the main issue.
I have hired lots of people who ventured out on their own, then (for whatever reason) decided to become an employee again.
One thing that I always worry about when hiring someone in that situation is - what is the chance that they will leave soon to try again? I spend a lot of time talking about that with candidates during their interviews. I don't want to hire someone for a short time while they gather their thoughts, only to have them venture out once again. I like to only hire folks who will be around for a while.
If you end up in that situation, you want to be clear in your own mind what you want to do - start another business eventually, or give up the idea and go back to being an employee.
If the former, you might consider being a contractor for a while, rather than a permanent employee. As Joel Etherton wisely states in his comment: managing contracts and billables and invoices and all the other lovely things about it help prepare people for the business side of things.
If the latter, then you want to be clear in your own mind how you can convince a potential employer during interviews that you really do want to be an employee again.