Renewing my dDriving ler's License p: Part 1

MThe expiration date of my driver's license expires was coming soon.

So, I went to police station, but I had to take a 2 two-hours lesson becaussince I had a traffic accident before.

I'm assuming that you had an accident before. Are you implying that you had a traffic accident near the police station, or are you just stating that you had a traffic accident before?

That was totally my fault due to my carelessness and distracted driving.

I combined the because clause from your next sentence.

Shortly, I hit my car to thea car in front of me.

Unless you're explicitly saying that you're using someone's else car, I'm assuming that you're using your own car to drive.

In the car, there were two elementalry school kids and the driver was their mother.

Corrected spelling of elementary

Fortunately, allnone of us had not had anyve been injuryed.

I really felt sorry for the small children who were in shocked at that time.

Then I swaore to the sky,myself that I don't want to happen suchexperience a terrible accident again.

I never ever belittleliked driving.

I'm confused if you're saying that you don't like driving or if you mean to say something else.

tTo be continued…

My driver's license expires was coming soonwas about to expire.

"driver's license expires" is incorrect, maybe "expiree" could also work, but the way I phrased it is more natural sounding-

So I went to the police station but I had to take a 2 hours lesson because I had a traffic accident before.

"2 hours lesson" is incorrect because whenever something is a "x hour noun" you don't need the "s"
example:
"2 hour cooking video"
"2 hour movie"

That was totally my fault.

probably a typo

Because ofDue to my carelessness or distracted driving.,

more natural

Shortly, I hit my car toI hit the car in front of me.

"I hit my car to the car in front of me" is very unnatural and grammatically incorrect, you don't need to state that your car hit the other car-

In the car, there were two elementalry school kids and the driver was their mother.

probably a typo

Fortunately, allnone of us had not had anybeen injuryed.

"none of us had been x" works better than "all of us had not been x" whenever x is a 0 amount
examples:
"none of us had eaten yet"
"none of us had the flu"

meanwhile you can use "all of us" whenever x is a max amount

if all of you were injured then you could have said
"all of us had been injured"

I really felt sorry for the small children who were in shocked at thate time.

"in shock" (a state of shock) or "shocked" (a state of shock)

Then I swaore to the sky, that I don't want to happen such a terriblecause another accident again.

I will never ever belittle drivdrive carelessly againg.

"belittle" means to think or talk badly of something to the point of derision such as thinking that a person is not worthy of repsect.
"The kids at school belittled me all the time"
"My mother belittles the way I cook"

It sort of works in this sentence, but it implies that you thought that driving was a useless activity, which I don't think was your intention.

My driver's license was expires was coming soon.

This is more idiomatic. If you wanted something similar to the original, note that "expires" is not a noun and you would need to say "expiration date."

So I went to police station, but I had to take a 2 two-hours lesson because I had had a traffic accident before.

Avoid beginning sentences with "so."
The traffic accident happened further back in the past, hence "had had."

That was totally my fault.

BIt was because of my carelessness or distracted driving.

Alternatively, you could have combined this with the sentence afterwards.

Shortly, I hit mMy car hito the car in front of me.

"Shortly" should be used if you're describing one event happening after another.

In the car, there were two elementalry school kids(students), and the driver was their mother.

"Kids" is fine, but this phrasing is more natural to me.

Fortunately, allnone of us had not had anywas injuryed.

More appropriate phrasing.

I really felt sorry for the small children who were in shocked at thate time.

Then I swaore to the sky, "I don't want to happencause such a terrible accident again."

I never ever belittltake driving lightly.

Or, "I take driving very seriously."

tTo be continued…