Should parents pay to their children to do home dutiuse chores ?

Chores is better suited for this context rather than duties.

Some parents pay to their children to do some chores inat home.

"At" better expresses location than "in".

They wantould like to teach their kids to earn money and spend it with responsibilitly.

"Would like" is a more formal and polite word than "want".

TSimilarly, they think that, show toing children to work for what youthey want it is an important lesson, they think that. Furthermore, with this kind of example children can become a responsible adults.

Children is plural hence "they" is used rather than "you".
Make use of linking words to avoid repetitive words.
Furthermore is a linking word used to add onto a point avoiding repetition of words.

On the other hand, many parents do not think that pay toing children to do their dutichores is a good idea, becaus. They believe every family member should help with homuse chores selflessly due to them ar, as they are apart of the family part.

None

TMoreover, they believe that children should learn to take care of home fortheir homes out of love and respect tofor their family itand not because of money.

"Homes" is used as Children is plural.

In conclusion, every family haves their ways to of teaching values to their children, with their own perspective s ofn what it is worth it in life.

Family is single noun hence "has" is used instead of have.
I did not want to change your sentence but I would have used "important" instead of " worth it" in this context. :-)

Should parents pay to their children to do chome dutires?

What you call home duties would usually be just called "chores." :) You could also say "household chores" if you need to specify but thats a bit formal.

Some parents pay to their children to do some chores inat home.

No need for some. It sounds awkward somehow. And it's always "at home" never "in home." You can say "in the house" for some situations (e.g., "we don't wear shoes in the house") that refer to the location inside the house more than they refer to the idea of being at home.

They want to teach their kids to earn money and spend it with responsibilitly.

They think that show toing children tohat they should work for what youthey want it is an important lesson, t. They think that with this kind of example children can become a responsible adults.

These phrases are a bit awkward but technically correct as I wrote them, I believe. Here's how I'd rephrase to make this sound more natural:
They think that it's important to teach their children that they should work for want. They think that they can help their children become responsible adults by setting this kind of example.

On the other hand, many parents do not think that pay toing children to do their dutichores is good idea, because every family member should help with home chores selflessly due to them aresince they're a family part.

Mostly correct! I'd rephrase like this to sound more natural:
On the other hand, many parents don't think that paying children to do their chores is a good idea because every family member has a responsibility to help out at home.

They believe that children should learn to take care of the home forout of love and respect tofor their family it, not because of money.

In conclusion, every family have theirs ways to teach values to theirits children with theirs own perspective ofon what it is worths important in life.

Sorry for the big rephrase, I just didn't know how to communicate what you were trying to say without building the sentence a bit differently.