If you and your mother both wish that your mother signs over the house to you then you need two independent solicitors.
One advising your mother (who will probably tell her she would need to be wary about signing away her assets, if she needs further paid care into her old age).
You need to be aware you may need to pay gift tax if you go over your life-time limit of inheritance. Your solicitor will help you with that.
You don’t need to know if your mother has a will or an enduring power of attorney in place but it probably would be good for family relations if you, your brother and your Mum were all in a harmonious family relationship and able to discuss such matters openly. If your Mum has a regular solicitor she may have been putting all of this in order in the last few years.
However if your Mum said to you, move in with me and mind me into my old age and I will give you the house and this is not in writing you might be better off if you had never moved in. A verbal promise is meaningless if one party starts to backpedal on it. (I am making an awful lot of assumptions here). So do you have anything in writing? Do you pay your mother rent, do you pay household bills, are they in your name? Do you have an agreement about anything. Did you Mum say 17 years ago, move in and we will sort it out afterwards. And why did you not push then to sort it.
If you have lived rent free there for 17 years you should have good savings (no mortgage or rent), so maybe it is time to regularise your life and get your own house. When your mum dies you may or may not get an inheritance but either way you should not rely on it for large life decisions, such as where you live.
It may sound callous but you need to prioritise yourself and your family. Paying for your mothers carers all sounds fine if you and your brother can afford it indefinitely, but it sounds like your brother is already running into issues with affordability.
And what your brother pays, inherits, behaved etc is really none of your business, he can act independent of your wishes if he prefers. So keep him out of your plans. Your mother is free to leave him the house if she wishes, she may think that hosting you rent free for 17 years was sufficient. It does not matter her reasoning, she is free to make her own decisions.
I realise I have made a whole lot of assumptions and all of them are probably wrong, but the reality is you may end up with no home in the not too distant future unless you take independent steps to look after yourself and your family. You may wish your mother and your brother behave in different ways than they are currently behaving, but you cannot force that and you should not consider their actions as them treating you badly, their desires and wishes do not have to align with yours. So try to keep the emotion out of it and stay in good relationship with your family while accepting your wishes may not come true.