Legally speaking, it depends on your country's laws. In the US, it's your money and your parents have no right to it. That said, the amounts are so small that courts wouldn't bother with it anyway, so let's talk moral.
Is it immoral for a parent to have a right to her child's money? I say yes, it is immoral to take a child's money, no matter their age or how much the parent has provided that child. Parents have a legal and moral responsibility to provide for their children. If parents fail to provide, they can be thrown in jail. There are things a parent does not need to provide, like nice toys, but which nonetheless become the property of the child upon gifting.
The child has no choice but to accept the necessities (food, housing, clothing) which are the legal responsibility of the parent because children cannot sustain themselves. Child labor is outlawed, children do not have the education to support themselves, and employers would not pay children a living wage for their services. This is why parents have a legal and moral obligation to provide for their children, because it was a parent's choice to make a child and not the child itself.
Since there is no legal or moral obligation for the child to care for itself, indeed it cannot, then there must be some other legal or moral obligation which gives the parent a right to the money. A promise to repay is a legal obligation which would make lending the parent money acceptable. A child's carelessness which results in broken property (window, TV, etc) creates a moral obligation that the child repay. However, eating the food a parent must provide legally does NOT create an obligation for the child to pay.
Lastly, it is the child's CHOICE to work. A child is not legally required to work until that child becomes an adult. If a child does choose to work, it is for that child's personal benefit and not the parent. If a parent takes the money, the child could choose to stop working and the parent would have no say in the matter. Since it is the child's choice, to give up time and physical labor in exchange for compensation, then the fruits of that choice belong to the child.