The issue you will face is the concept of a gift with reservation of benefit - so if your mum gifts you half the house, but continues to live there and benefit from it, at her death the value (although not the legal ownership) of your share will count towards her estate for purposes of IHT and the 7 year gift rule will not apply, meaning even if she lives 15 years, its still counted.
There are two potential work arounds
1/ she pays you full market rent on your share, this would have to be done by the book, you would have to declare the rent as income and pay tax on it - this would make the 7 year rule and taper relief apply.
2/ There is no gift, if you have lived there for many years, not paid rent, but paid costs of maintenance, improvements, paid towards running costs, done work on the property, you can claim that you have gained a beneficial interest in the property and being put on the deeds formalises this, and therefore, in fact, there is no gift - you would need proof of the financial contributions and an accountant to go through it to formalise a paper trail.
An accountant specialising in estates is the best professional to get advice from, not a solicitor as they generally don't have the knowledge on the tax situation accountants have.
Also bear in mind that for care fees, should that become an issue, if your DM has made such a large gift, and if at the time of said gift she had reason to think she would need care (ie has a condition that could worsen etc) then it can be classed as deprivation of assets and the local authority can seek to reverse the gift and take the money anyway.