These sons/daughters of other Gods/Goddesses are also worshipped :
Aiyappa - son of Mohini (avatar of Lord Vishnu) and Lord Shiv
Yam - son of Surya/Sun God
Yami or Yamuna river - daughter of Surya/Sun God
Shani - son of Surya/Sun God
Daksha - son of Lord Brahma
Goddess Laxmi's sons
Narad - son of Lord Brahma
Lord Brahma's sons who are included in Saptarisis
Hanuman - son of Vayu/Wind God, however Lord Hanumanaji himself is considered as Rudravtar
Ashvins or Ashwini Kumaras - sons of Surya/Sun God
Also, all the sons of Lord Shiv are not worshipped:
Andhaka (son of Lord Shiv) is considered as notorious.
Actually posts are worshiped and so the one who hold the post. Ganesh (Head of Ganas, also known as Ganapati) is the prominent post since beginning or Aadi kaal (hence considered as one of the Aadi Devas) and must be worshiped before any other god.
Even as per Ramcharitmanas, Lord Shiv and Goddess Parvati worshiped Ganesh at the time of their marriage:
मुनी अनुसासन गनपतिहि पूजेउ संभु भवानी ।
कोउ सुनी संसय करै जानी सुर अनादि जिए जानी ।।
As per Shiv Purana (1.2.109):
There were various Ganeshas in different Kalpas. During the period of 'Shweta-Kalp', Ganesha was born to Shiva and Parvati, when they went to Kailash mountain shortly after their marriage.
Kartikey is worshiped because he became the chief commander or General of Gods' Army.
Similarly, sons of Surya, Yam, Shani and Ashvins (or Ashwini Kumaras) are also widely worshiped because they hold prominent titles like God of Death, God of Justice and doctors of gods respectively. Daksha and Narad, sons of Lord Brahma who hold the title of Prajapati and Devrishi respectively are also worshipped.
Each manvantar is ruled over by a Manu (a post not a name). In the present kalpa, six manvantaras have already passed and the names of the six Manus who ruled were Svayambhu, Svarochish, Uttam, Tamas, Raivat and Chakshush. The name of the seventh Manu, who rules over the seventh manvantar of the present kalpa, is Vaivasvat. The titles of the seven great sages (Saptarishi) as well as the title of Indra change from manvantar to manvantar. In current manvantar, Indra's name is Puranadar. In next Manvantar, these posts will be changed e.g. by the grace of Lord Vishnu, Virochan's son Bali will occupy the throne of Indra (according to Vishnu Puran).
Even Bali (son of a Ashur) will become Indra (worthy of worship) in next Manvantar. It really doesn't matter whose sons are worshipped and whose sons are not. Anyone who hold the title/post is worshipped no matter whether he is son of a mighter God or a Asura. If he doesn't hold post/title is not worshipped even he is son of a mighter God (e.g. Karna, son of Surya/Sun God). Originally described as the chief of evil spirits in Vedic-era texts, Kubera acquired the title 'God of Wealth' later and then people started worshiping him and he is depicted as demigod in later texts such as the Puranas and the Epics.