Please help me understand my nan's will

maman

My understanding is that if your mother receives PIP because of her disability then that would contue after she receives an inheritance because it's not means tested. 

As for any other means tested benefits she receives then she can reapply should she need them in future. 

GDB2222

Several people have stated confidently that mum has a vested interest, but I don't understand how they know that?

There's a lot of the will we haven't seen, and it's possible that your mum and her sister only gain a vested interest if they survive your grandad. So, if mum dies before grandad, it's possible you might still inherit.