what time should we arrive at the airport?

The time is arrival at the check in place.
NOT arrival to the parking entrance, the bus stop, the shuttle stop.
3 hours is the recommended time. This is summer peak travel and the Airport is busy with many flights not just yours.
Suggest your Dads time of 7:30 while a little early does give you time to do what you need for boarding and then allow time for a meal before your flight.If you plan on taking something to eat or drink on board urge you to consume it on the plane as it might not be permitted past Mexican officials and taken away any of the leftovers.

NO NEED to plan on being the last person to board as they close the door and push off.
You are probably taking the Airport shuttle. It does not depart every minute. It can be full. Reserve your seats for the appropriate shuttle departure when you check in.

You should arrive atleast 2-3 hours early because traffic plus secuirty is awful

It's a good idea to be IN the airport about 3 hours before an international flight. So arriving around 8:30-8:45 would be plenty early. No need to be there as early as 7:30, and I'm someone who is generally early to the airport. But certainly no harm in arriving that early either.

Being at the airport three (3) hours before your flight is plenty of time.

I think your parents are making a > good < decision to stay at an airport hotel the night before. Try to get to the hotel during the early afternoon so you can all relax, use the pool, and otherwise make Friday the real beginning of your vacation.

Check the restaurant options for the terminal you will use. If there is not a restaurant that offers a real breakfast then eat at the hotel before taking the shuttle or taxi to the airport.

https://www.flysfo.com/shop-dine-relax/dining

8:40 would be fine, but if you want to get there earlier, go ahead.

You should be there at least 3 hours prior to departure for an international flight. If you want to be there earlier, that your choice.

Around 3 hours before your flight

3 hours before the time of the flight, for an international flight.

The general rule for an international flight is to be INSIDE the departures terminal at least 3 hours before scheduled departure, so there's no need to arrive at the airport before say 8.30. But it won't do any harm if you do, except that if you have luggage to check in, the desk might not be open for another hour.

I agree with W T Door that you should aim to get to the hotel on the Friday afternoon so it's worth while unpacking a bit and you can enjoy the hotel facilities.It also means you can relax knowing you're already practically AT the airport, and can't get held up in unexpected traffic.

You appear to live in live somewhere in the Bay Area...
Why are you staying at a hotel the night before? I know you are a kid and this is your parents decision but it seems really silly.
- People never sleep as well in a hotel instead of a own house.
- Your flight isn't until later in the morning, even if you lived in Stockton you could easily leave your house on a Saturday morning at 7am and get to the airport by 8:30...
- who wants to deal with getting ready for your flight at a hotel when your house has everything you need and you don't need to repack afterwards
- you can easily take uber from your house and then your car stays at your house instead of uber to hotel, shuttle/uber to airport...

I think you should tell your parents to skip the hotel... it is going to be a hassle.