Another approach would be to loan your mum the money and place a caution on the house deeds. So, effectively, you and your sister are providing a lifetime mortgage for your mum.
Either that or put the money in trust and then the trust lends the money to your mum.
You can change the will with a Deed of Variation and leave all the money to your children instead of to you and your sister.
If your grandmother died within the last two years then it is treated for inheritance tax and capital gains tax as though the change were made by your grandmother
If it is more than two years since your grandmother died then there may be IHT considerations if the money is not going to a direct descendent.
This explains what needs to be done:
https://www.gov.uk/alter-a-will-after-a-death
From there, the trust loans the money to your mum to help her buy the house and a charge is put on the property (just like when you get a mortgage) so that the house cannot be sold without repaying the money to the trust.
This will protect your grandmother's money from being taken for any care home fees.
Also, there is no problem with the children not being first time buyers etc as the trust is not buying the house but just lending money to your mum.