It depends on which "black" gene you're talking about. I can think of at least three that might be relevant:
The mother probably has Dominant White (turns black into white.) The daughter needs to get "black" (not-Dominant-White) from both parents, or else she would be white.
If the daughter has E (Extended Black, which makes a chicken have mostly black feathers), it only needs to come from one parent (the father). Since the mother has a lot of red or gold, she clearly does not have E (Extended Black).
To turn the black into blue, the daughter needs one copy of blue (probably from her father). Then she needs one copy of "black" (not-blue) from the other parent (probably the mother.)
If you mean that your Calico Princess hen has one copy of the Dominant White gene, and one copy of not-Dominant-White, then I agree that her daughter proves that very nicely.