Q: Mom is ill and can't care for my father right now. Do I need guardianship to move him in with me?
A: You want to be sure that there is some way to provide the best care for your father.
The best way to do that is for him to sign a durable Power of Attorney (POA). If he did not already do that and is no longer mentally competent to do so, then you will indeed need to have the court appoint a legal guardian and/or conservator to act on behalf of your father.
A "guardian" is usually put in charge of personal and medical decisions and a "conservator" would have the power to control and access the individual's money (bank accounts, retirement accounts, investments, etc.).
Once your mother regains the ability to care for your father, you can certainly allow her to continue to do so. The fact that you are the guardian will not prevent her from caring for your father.