@user6726 has provided a solid answer to the question of whether this conduct, if carried out by an adult, would be actionable. This answer addresses the additional issue of a parent's liability for the actions of their children (assuming that the conduct is actionable, which is actually an unresolved question).
In general, parents do not have vicarious civil liability for the acts of their children. In other words, unlike an employer who is legally responsible for any on the job conduct of the employer's employees, a parent is not automatically responsible for any conduct of their child.
There are some exceptions to this rule, although most of them clearly do not apply in this situation. In Colorado, some of the main exceptions are that:
The head of a household is responsible for the automobile accidents cause by driving a car belonging to someone in the household, whether or not the head of household or the driver own the car. This is called the "family car" doctrine.
A person who provides alcohol to underaged persons is responsible for harm caused as a result of the intoxicated state of the underaged person (to oversimplify).
A person is responsible for "necessities" (e.g. food or utilities or medical care) purchased by a spouse or minor child or ward of that person on credit, even if that person was not otherwise legally competent to make the purchase or did not have permission to make that purchase.
A parent or guardian of a minor is responsible for providing for the "support" of a child (who is either a minor or in some cases a disabled adult) and may need to reimburse someone who provided that to their child despite not having a duty to do so. For example, if a parent leaves a child at home and is stuck in a blizzard for a week and a neighbor provides food and housing to the child in the meantime, the parent is obligated to reimburse the neighbor for the expenses incurred.
A parent or guardian in Colorado is statutorily responsible for vandalism or graffiti caused by a child or ward up to a certain statutory dollar threshold.
A parent or guardian is responsible for harm caused by the parent or guardian's negligent supervision of their child, but this liability is imposed only if the parent or guardian failed to exercise reasonable care to prevent the harm.
Absent an exception, a parent is not legally responsible for the torts, breaches of contract and statutory violations of a child. In particular, a parent is not responsible for the business debts or business related liabilities of a child unless they result from negligent supervision of the child. Directing a child not to serve someone at their business is not the kind of conduct that is actionable as negligent supervision (a typical negligent supervision cases might involve a parent who saw the child put arsenic instead of sugar into the lemonade and failed to do anything to prevent the child from selling it causing someone to drink it and suffer serious injuries).
So, in this case, none of these exceptions apply.
Therefore, in this case, if the business is found to be a business of the child, the parent has no liability for illegal discrimination of any kind in connection with the child's business. The child could be sued and a money judgment against the child could be recovered from the child's own money and property, but not from the parent's money and property.
In the scenario presented in this question, determining if the lemonade stand was actually the child's business, or was instead, the parents's business in which the child was employed, would be a close one.
On one hand, if the parent paid for all of the materials sold in the lemonade stand, that would argue in favor of the business being the parent's. The fact that the parent had a de facto ability to order the child to conduct the business in a particular illegal way also favors a finding that the business is the parent's business. If the business is the parent's business in which the child is employed, the parent has liability under the statute if there is liability.
On the other hand, if the child paid for the inventory with their own money and the direction received from the parent was perceived as non-binding advice rather than as an order directed at the child, there would be a good case to be made that the business was the child's rather than the parent's. If the business is the child's business, then the parent does not have liability even if the child has statutory liability.
In reality, in many cases, there will be some facts that support the argument that it is the parent's business and others that support the argument that it is the child's business and the judge or jury will have to determine which characterization is most strongly supported by the evidence presented.