One of the famous names of Sri Ganapaty is "Skandapurvaja" which literally means "the elder brother of Skanda or Lord Karthikeya". So, Ganapaty is the eldest son.
Skandapurvaja -- One who is born (ja) before (purva) Karthikeya (Skanda).
108 names of Ganapaty,with 82nd in the list being "Skandapurvaja"
There is a Ganesha Asta Namavali Stotram found in the Brahma Vaivarta Purana.It was narrated by Lord Vishnu to Godess Parvati.That stotram has the name Guhaagrajam which has the same meaning as Skandapurvaja.
Vande Guhaagrajam Devam Sarvadevaagra pujitam/
Durgey Namaabhih samyuktam param,
Putrasya pasya Vedey cha tadaa
kopam thathaa kuru/
Yetanmaashtakam Stotram naanaartha samyutam
Trisandhyam yah pathennithyam sa sukhee sarvato
Tato Vighnaam palaayantey vaina teyaad yathoragah,
Ganeswaraprasaadena mahajnaani bhaved dhruvam/
putram Bhaaryaarthi vipulam striam,
Maha jadam Kaveendrascha
vidyaa vaancham bhaved dhruvam/
(Mother Parvati! your son has eight names viz. Ganesha, Ekadanta,
Heramba, Vighnanayaka, Lambodara, Shurpakarna, Gajavaktra, and
Guhaagraja. Please listen to the meanings of these names; this Great
Stotra is the essence of several Stotras and is the demolisher of all
kinds of obstacles
Sri Ayyappa was created from an union of Lord Shiva and Lord Vishnu (in the Mohini form), but he is not usually considered a member of Lord Shiva's family, however, in a Puja we do see his Pushpa Arcahna (worship by flowers) by the following Mantras which uses 8 names of Lord Shiva. :
Om Bhavasya Devasya Sutaya Namaha, Om Sarvasya Devasya Sutaya Namaha,
..... Om Mahato Devasya Sutaya Namaha.
So,he is considered as Lord Shiva's son.
Now coming to the question-Does Lord Shiva have a daughter?
According to the Padma Purana the answer is yes and her name is AshokaSundari
Ashokasundari (Sanskrit: अशोकसुंदरी, Aśokasundarī), also spelt as
Ashoka sundari is a character in the Padma Purana who is described as
the daughter of the deities Shiva and Parvati.
Ashokasundari was created from the wish-fulfilling tree Kalpavriksha
when Parvati wished for reducing her loneliness. The words in her name
are derived from her creation. "Ashok" refers to the easing of
Parvati's "shok," which means sorrow, while "sundari" means "beautiful
In Ganesha Pancharatnam, Adi Shankara also mentions Lord Ganesha as Puraripurvanandanam or the earlier (purva) son (nandana) of Purari i.e the enemy (ari) of the three cities (tripura) i.e of Lord Shiva.
पुरारिपूर्वनन्दनं सुरारिगर्वचर्वणम् ।
कपोलदानवारणं भजे पुराणवारणम् ॥४॥