In most traditional royal systems, the children of a female royal would generally be considered part of their father's noble house or dynasty, not their mother's. This is because royal lineages and titles are often passed through the male line, and the father's family name and house are usually considered primary.
In the specific example you provided, if Princess Charlotte of Cambridge were to marry a 'commoner,' her children would likely belong to the noble house or family of her husband, assuming he comes from a noble or aristocratic background. If her husband doesn't have a noble background, their children would likely not inherit any specific noble title or house.
For instance, the British royal family belongs to the House of Windsor, which is the dynasty founded by King George V in 1917. If Princess Charlotte married someone from a non-noble background, their children would not inherit any royal titles or be considered part of the House of Windsor. However, they would still have a connection to the royal family through their mother, who is a member of the royal family.
It's important to note that customs and rules regarding royal titles and nobility can vary significantly between different countries and cultures. Each royal family may have its own specific traditions and rules governing titles, succession, and membership in noble houses.