Can my mom sue after she suffered fall and concussion at hotel in another state?

Yes, if there was an unreasonable condition that caused her to fall.

Of course. However, she will need a lawyer in the state where she fell, and she will be required to prove that the hotel did something that it should not have done, or failed to do something that it should have done, which CAUSED your mother to fall. Otherwise, she will lose. Each state has its own set of rules.