Any debts due from an estate have to be paid out from that estate prior to the remainder being distributed in accordance with the term of the will.
So, if your mother had owed £600 to the tax man at the time of her death, that sum would have had to come from her current or savings accounts (or similar) BEFORE the estate could be distributed to you and your sister. That would, in effect, reduce the amount that was payable to your sister.
Similarly, if your mother had left the money in her savings account to Battersea Dogs' Home, your sister would have had to be paid the £600 BEFORE the distribution to the dogs' home could take place.
So the legal position now is that your sister must be paid £600 from your mother's account BEFORE the estate is distributed. That, obviously, will mean that there will be £600 less in the account for her to then inherit under the provisions of the will.
So I agree with you. If she takes the money from the proceeds of the house sale, she'll be getting it twice.