[SqueakyRat]

Hi there,

Just a few minor spelling mistakes this time, your cases are all correct.

NOM：The child is small. = Das Kind ist klein.

Correct.

GEN : The hat of the child is blue. = Der Hut des Kind ist blau.

[des Kindes]

DAT : The textbook belongs to the child. = Das Lehrbuch gehört dem kind.

Probably just a typo, not a real mistake, but it's Kind.

AKK : The mother is holding the child. = Die Mutter hält das Kind.

Correct.

NOM : The children go to school. = Die Kinder besuchen die Schule.

Correct.

GEN : The teacher of the children is young. =Der Lehrer der Kinder ist jung.

Correct.

DAT : We helped the children to get in the car. =Wir haben der Kinder in den Wagen geholfem.

Just a few spelling mistakes. [den Kindern] and [geholfen].

One of these days I really have to try to explain when to use what word ending and so on, but it's really difficult to explain it in english for me, everytime I have some half-baked explanation in my mind I think to myself "Nah, I think of something better next time" but I just feel a little bad when correcting a sentence without really explaining why it was incorrect before.
Then again, seeing as you got it right in most sentences you don't seem to have too much trouble with this anyway.

AKK : The big backpacks hinder the children walking. = Die großen Ruchsäcke behindern die Kinder wandern.

You've got a typo there, it's Rucksäcke.

Other than that, just squeeze the word [beim] in between Kinder und wandern and you're good to go.
Oh, and since you've got an article with beim (bei dem) the verb wandern is transformed into a noun, so you start with a capital letter.

[Die großen Rucksäcke behindern die Kinder beim Wandern.