my mother wants to sell me her house under value which I have accepted to do, it will leave me with 50,000 in bricks and mortar as inheritance, she wants to give brothers 20,000 each, to which one has said he will not accept this , my brothers have not treated my mother well over the years and this is her decision, she has doctor signed papers to say she is fit to make decisions as she is 87 yrs old,, can my brother stop this sale?

Not unless they can prove she isn't fit to make those sort of decisions. Its her property to do as she wishes, theiirs... unless its already part of a irrevokable trust.

Legally she doesn't have to give them a dime when she dies.

No it isn't under any trust, and everything is going through the solicitor as it should, the house is valued at £120,00 and I have buying it for £50,000.
The doctor has signed all the questions the solicitor wanted as being fit to make decisions.
He is now bullying her saying he will buy the house off her and telling her that I will throw her out of the house etc etc,, which I would never do, mum is getting more and more upset over this and I am worried about her health, I will take her to the solicitors on Monday to let them know what he is doing,, but if I can assure my mum there is nothing he can do to stop her she should be OK,, thank you

Do most definitely take her to the solicitor... anything that will put her to ease, and at 87.. she doesn't NEED that sort of agrivation. If she hasn't already... please get her to prepare and file her Will. If she would die without one I can see the problems that would cause.

They could still contest the will... but its still better than not having one at all.

Yes she is about to sign a will and the solicitor has also got her to make a statement as to why she doesn't want to give the two brothers any more money,, this was very difficult for her to do at 87 yrs old as she feels ashamed that her sons are like they are, as I am sure that they will contest when the time comes,, thanks once again for yr reassurance

In the US you can't sell a house to anyone, even a child, for under market value, without being gift taxed on the difference. It is better tax wise to leave a house in a will (she can certainly leave it to you!). Not the same where you are? One option here is to write a family loan at government set rates and to gift the annual maximum (here 13,000). It helps a lot to have an appraisal done by a certified appraiser, not just some real estate agents.
Again, I'm talking about the US.
It sounds like she has a good solicitor and he will also be helpful later.

Its somewhat the same here in UK, when I ever sell the house I will have to pay capital gains tax,, this is something I have to keep in mind and yes she would be better keeping the house until the will BUT with the brothers I have they keep asking her for money etc etc and also the house needs a few repairs which she cannot afford,, its in her head that she wants to sell it to me so I can also evenutally live in it, she has been in the house for 55 years now.
She says that if she leaves more to me in her will then she is still leaving behind them contesting the will and says she wants to go knowing that it has all been finalized, she is a tough old bird and her ideas can't be shifted, lol

One other point here is, if mom is concerned about you forcing her to move, you may be able to give her a life estate, again not sure of the laws where you are (I assume the UK but ANY question on law needs to include your general locale as laws vary by area.) but the US allows a sale of property with a guarantee that the previous owner can continue to reside there as long as they are physically able.

Yes we are getting a contract drawn up to say that she can live in the house for as long as she is able,, also that if she needed 24/7 care in her own home that I would move in with her to care for her (as I am a trained palliative care carer) !

Frankly, I think mom is lucky to have you as a daughter. Good luck with this.