A sSpecial mMemory with mMy fFamily

Generally, all words in a title are capitalised, with short prepositions being one exception. "With" is considered short by some style guides but not by others, so you can either capitalise it or not depending on your preference.

This memory was from when I was a teenager and I lived in my parent's' house.

(1) I removed the second "I" to avoid unnecessary repetition of the word.
(2) "Parent's" is singular; "parents' " is plural. For the possessive form of plural nouns ending with "s", we will generally just place an apostrophe after the word, without the additional "s" that typically accompanies it.

Since I was a kid, my parents (have) taught me the love forjoy(s) of traveling in our car; with: stopsping, visiting new places, tasting foods on the way to our destination.

(1) I'm sceptical about the use of "love" with "taught" in this context. "Joy" or "joys" will be a more appropriate word here.
(2) Here, the colon is more appropriate than the semiciolon, because what follows after is an elaboration of said joy. While this is a simplification and not entirely accurate, you might think of the semicolon as somewhat equivalent to the full stop.
(3) I changed "with stops" to "stopping", so as to better match the word form of "visiting" and "tasting". I think it will sound more natural and fluent this way.

We started in Bogotá, Colombia's capital, and our destination was to go to the Cabo de la Vela.

(1) In this grammatical structure, the two commas typically exist as a pair.
(2) "Destination" refers to a place, not an action; "the Cabo de la Vela" is a place, while "to go to the Cabo de la Vela" is an action.

The last is a wonderful place in the tip of Colombia.

Alternatively: "The latter is a wonderful place in the tip of Colombia."

The distance between Tthe Cabo de la Vela and the capital Bogotá is one thousand, one hundred and twenty kilometers.

(1) "The" isn't part of the name and shouldn't be capitalised.
(2) If the full spelling of the number is long, as it is in this case, we'd just use the numerals: "1120 kilometers".

So, on the way, we livehad many experiences, bad and funny moments.

Perhaps you meant to say "we lived through many experiences". However, note that "live through" is used only for unpleasant experiences.

When we were almost arriving ato the Cabo, a military manofficer give us an alert.

(1) The phrase is "arrive at".
(2) "Military man" is fine, but "military officer" would be the more exact phrase to use.

He told us that if we decided to continue driving ion this street, it would be our own responsibility if something bad happened withto us.

(1) The phrase is "drive on (a street)" or "drive down (a street)".

(2) I think the phrase "happen to (someone)" would be more appropriate here. In my experience, "happen to" typically emphasises the actual thing that occurred, while "happen with (someone)" places more emphasis on an outcome or state. For example:

> "What's happening to you?" ("What is the thing that's affecting you?")
> "What's happening with you?" ("Why are you in such a state?")

The difference can be very subtle, so don't worry too much about it if it's not too clear at this stage. It will likely come with exposure.

It was scary, but my father decided to continue, because he (had) met other people that had made their trip safely.

If the meeting occurred very close to the time your father decided to continue driving, and in the same location, then your original sentence is correct. If the meeting instead occurred before you reached this part of the road, whether that was before you even began the trip, or in a restaurant just 10 minutes ago, the past perfect tense ("had met") would be expected.

We drove a few kilometers, then a car passed us in the opposite direction, with four people with masks.

(1) The two use of "with" in such close proximity might not be ideal. Alternatively, you can consider: "then a car passed us in the opposite direction sitting four people with masks." Here, "sitting four people" means that the car is holding four people.
(2) Just for your information, here's a nice grammatical structure you can also consider here: "We drove a few kilometers before a car passed us in the opposite direction sitting four people with masks."

We visited different places ion our return to the capital, and we had a scary anecdote.

The word to use with trips and journeys is "on": "I stopped by the shop ON my way home"; "I met many people ON my journey"; "I saw a deer ON my hike up the mountain", etc. You had applied this when you wrote "on the way" in a previous sentence.

With the time, we learned that you need to pay for a tour to visit this place, with security and more people.

The phrase is "with time".