Was Ishmael a teenager or a child when he and Hagar were sent away by Sarah?
It is reasonable to say that Ishmael was 18-19 years old when Abraham send him and his mother Hagar away.
Why?
Ishmael was circumcised at the age of thirteen, Abraham was 99 years old, Vs 24,25 below
Genesis 17:23-27 (NASB)
23 Then Abraham took Ishmael his son, and all the servants who were
born in his house and all who were bought with his money, every male
among the men of Abraham’s household, and circumcised the flesh of
their foreskin in the very same day, as God had said to him. 24 Now
Abraham was ninety-nine years old when he was circumcised in the flesh
of his foreskin. 25 And Ishmael his son was thirteen years old when he
was circumcised in the flesh of his foreskin. 26 In the very same
day Abraham was circumcised, and Ishmael his son. 27 All the men of
his household, who were born in the house or bought with money from a
foreigner, were circumcised with him.
When Abraham was 86 years old Hagar gives birth to Ishmael and when at the age of 100 years old Abraham, his son Isaac is born. Hence Ismael is 14 years old when Isaac is born.
Genesis 16:16 NET
16 (Now[a] Abram was 86 years old[b] when Hagar gave birth to
Ishmael.)[c]
Genesis 21:5 (NET Bible)
5 (Now Abraham was 100 years old when his son Isaac was born to
him.)[a]
The scriptures do not state the age at which Isaac was weaned, on the day that Isaac was weaned Abraham prepared a great feast.
Genesis 21:8-9 New English Translation (NET Bible)
8 The child grew and was weaned. Abraham prepared[a] a great feast on
the day that Isaac was weaned.[b] 9 But Sarah noticed[c] the son of
Hagar the Egyptian—the son whom Hagar had borne to Abraham—mocking.[d]
From Google
Is it OK to breastfeed a 5-year-old?
For the rest of the world, it's very common that toddlers 4 to 5 years old still are nursed by moms for bonding and health reasons. The World Health Organization recommends breastfeeding babies up to two years, precisely because of the breast-cancer-prevention benefits. June 22, 2008
Conclusion.
In many parts of the world, today toddlers are breastfed to 4-5 year, so about four thousand years ago at the times of Abraham and taking into consideration the different lifestyle of that period, without the hustle and pressures of today, Sarah most probably weaned Isaac from 4-5 years
Hence it is reasonable to say that Ishmael was 18-19 years old when Abraham send him and his mother Hagar away.