In order to improve the living standard of their families, both parents go to work everyday.
I suppose Joy Lin is right. This first sentence lacks gusto. You can change it a little to include an unexpected idea and really catch the reader's attention.
Also, in this sentence you need to have every day as 2 separate words.
It is like this:
Both of them go to work every day.
Going to work is an everyday activity.
("Everyday" is an adjective.)
Moreover, a family that has a stay-at-home parent generally has more happiness [. . .]also contribute to the society as well.
If you say something like this, it is important to include a citation. Cite the source where you found this fact.
Also, if you want to make this a stronger argument you can write about what someone would say to disagree with you (i.e. the counterargument). Then, refute the counter-argument.
Your grammar is excellent!