I don't want his mother to tell a lie to him to hide the truth.

=>I don't want that his mother will tell a lie and hide the truth from him.
It's advisable for her to explain this situation in a roundabout way, like "Something wrong happened to Daddy, so he can't help living apart from you."

=>It's advisable for her to explain the situation in a right way like, "Something wrong happened to your daddy, so he had to live far away from us.
The son and his father can have a relationship through letters.

=>Father and son can still have a good relationship through writing a letters.
All men are liable to err, but have to take the consequence.

=>All men are liable to err, but they have to take the consequences.
We can be more mature if we are able to learn how to overcome a difficulty.

=>We can be more mature if we are able to learn how to overcome difficulty.

I know the fact that family members should share the pain with each other.

=>I know that family should share their problem with each other.
However he is so young that he can't accept(or understnad) the truth. It takes time.

=>However he is too young that he can't accept(or understnad) the truth. It takes time.
She should tell the truth later not to suffer psychological damage.

=>She should tell the truth in order not to suffer psychological damage.