"Average age .. is around" would be correct but not "average age .. is at."
Meanwhile, the "is" in "24 year-old brother is" would be unnecessary so you can drop it.
"The average age of instructors at the gym is around 22 years old, which is younger than my 24 year-old brother."
You correctly switched between "old, which" to join to sentences and "old. They are" to separate the two. Together or separate are both correct in the forms you used.