Yes, beneficiaries of a will can gift part or all of their inheritance to anyone they wish.
But having a deed of variation drawn up means the money is treated as though it had been left directly to the recipient of the gift.
A gift of £100,000 to an adult child exceeds the UK standard annual gift allowance, which is £3,000 (or up to £6,000 if you did not use the previous year’s allowance).
Instead, the future IHT tax status of a gift of £100,000 may potentially be tied to the 7 year rule. If the parent dies within 7 years of making the gift, the £100,000 is brought back into their estate for evaluation for IHT.
The better plan would have been for the executors to approach all the beneficiaries of the will and obtain their agreement that a deed of variation is put in place in order that £100,000 of the £200,000 left to the mother could be paid directly to the OP.
That way, the OP receives an inheritance which is not potentially subject to the 7 year rule, as it is treated as though the original will had left the money directly to her.
The OP has not received an inheritance from a "distance relative", she has received money gifted to her by her mother.
A deed of variation can be applied retrospectively within two years of a death.
For more information:
https://www.moneyhelper.org.uk/en/family-and-care/death-and-bereavement/gifts-and-exemptions-from-inheritance-tax
https://www.gov.uk/inheritance-tax/gifts