I do not think putting your name on the deeds will make a difference, the only way the house would not be taken into account would be if you lived there and owned 1/2 of it. If there is a co-owner who has the right to live in the house it's value is effectively zero so it is not considered an asset. So will not be used to offset care home fees.
They do not actually force you to sell the house now , but a charge will be put on it that has to be paid back when it is eventually sold.
For advice about this contact 'AgeUk' the charity , they have specialist advisers who can tell you all the legal ways to avoid care fees from property owned by people who need to be put into care.
But do it now ! with care home fees at a minimum of £600 a week the house value will not last long ! If your Mum was ever to need '1 to 1' 24/7 care the fees are from £3000 per week !