What are the chances of a plane engine failure or a plane crash? What was the most recent one?

And your fear is based on what facts? People fear what they do not know. Fortunately there is a lot of info on air safety and fear of flying. Read up on it. You don't need to read about plane crashes. Read about how air travel is the safest form of travel available.

Airplane rides are inherently safe if you have a good pilot like Capitan Gatito at the control.

You're going to be ok! The chances of an engine failure or crash are extremely minimal, contrary to what the media would have you believe. Most pilots will go their entire career without having a total engine failure. I'm not saying it doesn't happen, as it has happened to me once, but only once in thousands of flight hours and even then we made it down safely and gently. Pilots like your dad are well trained to handle emergencies in the air and your odds of being in a crash stand about where your chances of being struck by lightning do. Like I said, it would be dishonest to say it never happens, but it's not a stretch by any means to say that you'll win the lottery before you're in any significant crash. All pilots are trained to land the aircraft safely should the engine give out. It is a procedure that is drilled into our heads early on, better to have and not need than need and not have. Taking a long flight to Mexico with your dad would be an excellent opportunity for you to learn about the realities of flying. A lot of people feel as you do until they get a chance for a hands on experience. By the end of the flight you might even want to become a pilot yourself. It's the greatest freedom you will ever have. Your dad, like any pilot, will go over his aircraft top to bottom before he allows any passenger on board, let alone his own child. You can take comfort in something that gives pilots pains, the fact that aircraft are subject to extremely strict maintenance requirements which ensure that our aircraft remain in good flying condition. The most recent accidental crash was the Palo Alto incident. A lot of things went wrong during that flight, not the least of which was the pilot taking off into heavy fog. Although that is not illegal, most instrument pilots avoid weather where you can't see the ground because sometimes you take off and have to turn around and land in the same spot immediately. The decision to take off is optional, landing is not. There is no way your dad is going to take a risk like that with you on board and there was no valid reason the Palo Alto pilot should have done it either. You're going to be just fine. Enjoy your trip to Mexico, be careful about drinking the water.

the most recent one was today but that was because of the damn IRS not engine failure

In one year, there are 43000 automobile deaths in the US. On average, 135 people die in airliner accidents in a year. You are over THREE HUNDRED times safer in an airplane than a car... The most dangerous part of your trip is the drive to the airport.