If your mother rents out part of her home, and she is the only owner of the home, then the rental income is her income. Being her daughter doesn't make it your income. Forming an LLC doesn't make you or the LLC an owner of the home, and it doesn't make the income your income or the LLC's income. The rental income is still your mother's income, and she has to report it on her tax return.
Also note that a single-member LLC is disregarded for federal income tax purposes. In other words, as far as federal income tax is concerned, the LLC doesn't exist. You and your single-member LLC are one and the same. The LLC's income is your income. So it's not clear what would be accomplished by forming an LLC.
Why do you want to report your mother's rental income on your tax return? What are you trying to accomplish?
I would add one word to Mike9241's warning about adding you to the title. It could result in a huge tax bill for you.
