Grammar, Apostrophe – Where Should the Apostrophe Go in ‘Three Days Work’

I think it's useful to substitute "child" and "painting" because child is a word where the plurals and possessive forms are more obviously different.

What would be the correct label for a picture drawn by several kids?

1. Children Picture
2. Child's Picture
3. Children's Picture

I think the third - the possessive plural. This suggests that "Goats' Milk" is the correct label for the milk.

This is a somewhat archaic construction. The more modern way to say the same thing would be

It took the prince three days to die.

In my mind, the "was [timespan] dying" construct does serve to emphasize the fact that the person was dying the whole time, rather than "working up to it" in a sense.

(And just to be perfectly clear, yes, it does mean that the prince is now dead.)