Fortunately and by grace tothank God, we could repair the car and continued with the trip.

It was a trip around 12 hours, sometimes(and on the way) I sayid to me "return tyself "I need to go home", however I saw my children´s face and Ttook the decitsion to continue.

some of the corrections are there to make it sound more natural in my ears

When We arrived to hotel, I felt more quietcalmer and happyier, because we had overcame the challenge.

The next day, we went to zoo atin the morning; atin the afternoon we went to the "turi Mirador".

On sunday, we went back to home, and by grace of God, all the thank God everythings we did were goognt well.

Thanks for your help for reviewing this letter.

Almost without thinking, my family and I decided to travel at the last weekend.

No need for "at the" here. Same thing for if you were talking about "next week", like "I will travel next week".

It was a strange trip, for example the car showed a damage in the transmitssion systems.

Damage will never be "a damage". Damage is very...general, unspecific. You may say "A scratch" or "A dent", but not "a damage".

"in the transmition systems." --> "in the transmission systems." Just a minor typo! I could see native English speakers making this one too.

Fortunately and by, by the grace tof God, we could repair the car and continued with the trip.

It was a tripThe trip was around 12 hours, sometimes I sayid to me "yself "I want to return to home", however I saw my children´s faces and Tookmade the decitsion to continue.

"...sometimes I say to me..." --> "...sometimes I said to MYSELF..." (Past tense. But also, when the action is 'reflexive' (you doing an action to yourself), it is "myself".
For example, "Look at myself", "Talked to myself", "Fed myself". If someone different said it to you, then it would be "said to me"

" "return to home"" --> ""I want to return home"" OR "Return me to home"" (Could be many ways of wording this. Just feels like it's missing an element of desire, or want)

"I saw my children´s face" --> "I saw my children´s FACES" (Assuming from "children" that there is more than 1. Same applies to the word "face". Each child has a face, there's more than 1 face, so it is "faces"!)

When Wwe arrived toat the hotel, I felt more quietcalm and happy, because we had overcome the challenge.

use "at" with "arrived". You are already at the destination in this sentence, not "going TO" the destination.
It is "The Hotel" because hotel is otherwise a general word that could be many hotels. "THE Hotel" implies it is a specific hotel, and indeed, it is specifically the one you went to!

Would use "calm" instead of "quiet" in this instance. Calm is more...relaxed, not stressed, etc. Quiet is used more for volume, sounds, noise.

" because we had over the challenge." --> " because we OVERCAME the challenge. (I'd consider this advanced English vocab, nice!)

The next day, we went to zoo at the morning; at the afternoon we went to the "turi Mirador".

"The Zoo", for the same reason as "The hotel" in the previous sentence.

"IN the morning", because I suppose we see ourselves as "inside" that period of time. I suppose it is strange that we say "at night" and "in the morning"!! 😅

On sSunday, we went back to home, and by grace of God, all the things we did were googd.

Days of the week are always capitalized - Sunday, Monday, Tuesday...etc