Sure, it may make no sense but that does not mean it did not happen. In my line of work, I've seen inexplicable actions by many people during times of illness and crisis, and they are usually reacting to slights in the past. Maybe it was because of tension between Alice and Frederika in the past that Frederika instructed no one to tell Alice, or she might have done it because of problems between the two princesses and she thought Ellen's wishes were being honored. Alice was certainly responsible for her share of hurt feelings but there is no denying that near the end of her life, Alice devoted more time to spiritual beliefs and perhaps, just perhaps, she wanted that last chance to see Princess Nicholas. After all, they were the only members of the Greek royal family to remain in Greece during World War II.
With the exception of Marina of Kent (who I must confess might have told Alice but perhaps she had more pressing worries like the imminent death of her mother and can justly be excused for not telling her), who else in Alice's British family would have known about Ellen? I daresay none of them would have, not even Prince Phillip, and it has never been implied that they knew anything until Ellen died. Thus, the information was known by the Greek royals, of which Alice was still a member of the family.
That being said, I love these discussions and I guess we will never really know all of the facts surrounding this very human family during the final illness of one of its members.