You will need a power of attorney. In that case, you can complete the tax return but you can't e-file. Print and file by mail, sign your mother's name then "poa" and your name, and attach a copy of the POA to the return when you mail it.
If using TT online, you will need a separate account, since each account can only file one return for one person. It may be more cost effective to use Turbotax installed on your own computer from a CD or download if you need to file more than one return.
If you don't have power of attorney, you will need to go to the surrogate's court and have yourself named as your mother's guardian. Hopefully though, you did some advance planning when your mother was diagnosed but while she was still competent.
