Can a child inherit both their parents' clans jutsu? Can a child in Naruto inherit both abilities from his parents' clans?

For example, if Ino and Sasuke had a child is there a possibility for it to have both Uchiha's Sharingan and Yamanaka's mind transfer jutsu?
Yes, a child can inherit both clans' jutsu.

This was officially explained by Masashi Kishimoto(the creator of Naruto)
The child with an Uchicha and a Hyuga as parents will have both the clans' eyes.

While Inojin is not a good example as the techniques of his father Sai were taught to him.The Ninja art techniques are not passed via genetic inheritance.
Also, Ino's clan techniques are classified as Hidden techinques which use Yin/Yang release which are also taught/learned not passed via genetics.

A good example would be an Uchiha + Hyuga child as answered by Kishimoto himself -