Question

Which is correct parents should or parents must look after their kids?

Answer 1

Both are correct

Should means not too very important like you should bring book so it's easy to learn

Must means very important

You must bring books or you won't write the exam

Here you can take must cause they must take care

Answer 2

both are correct. as

they should not relay so burden upon their children

and even children should obey words of their parents and to learn from them to how to face society