Your mum should definately see a solicitor to help draft a will, and if the house purchase goes ahead to act as her conveyancer.
You and your mum should include your brother in all of this as well so that he is aware that it is all fair and even. (I'm not saying you aren't already)
Regarding the stamp duty, you will have to pay this at the proper valuation, which if you are buying with a mortgage the valuer that the mortgage company sends will provide.
In the past a friend was in the same situation buying a property for their daughter, and then selling it to them (at a reasonable price) and the taxman came calling for what they believed to be the stamp duty for the correct value.
You will need a solicitor to act on your and your mortgage companies behalf for the purchase.
A financial advisor may be able to give some guidance as to the best course of action.
Best of luck with it.
Sparky