Who bought the cucumber??
What has that got to do with anything? Do manners boil down to money? It's ok to destroy something as long as you, or your mother, paid for it? How is a child meant to know who pays for what, and why should she care?
Taking the post at face value, and assuming that there is nothing else going on that wasn't mentioned (struggles over eating, or something of that nature), it seems to me to come down to a difference in approach about acceptable toddler behaviour.
In the daughter's home, where she is the 'head of house' (for want of a better way of putting it) she is within her rights to do things her own way, but in someone else's home, there should at least be a discussion about what is acceptable - both from the adults, when it comes to discipline, and from a small child, who looks to the adults for guidance.