Radiator fan not staying on when AC is on, causing car to overheat

I'm not sure how to tell if the brakes are locking up or not. This only happens after I've driven the car for a little over 20 minutes. And it doesn't even happen every time. What could cause the brakes to lock up at around the same point each time? Bc like I said, this never happens in the earlier portion of my commutes.

Also, one person who looked at my car said that the transmission fluid smelled burnt. Should I flush it, clean the filter, and add more fluid before considering a new transmission?

You're right. I do have no idea what's wrong with my car. My first concern was whether the fan was supposed to stay on while the AC is running, like it does in most cars. I figured if the fan was faulty then maybe it was the cause of my other problems as well. If the fans are functioning normally for my car, then my next guess would be that something is wrong with the transmission. I'm going to call a hyundai dealership tomorrow to inquire about the fans, bc I don't know how else to find out what is normal for my model of car, other than asking someone else with the same car. One mechanic told me that some radiator fans (such as certain Volkswagens) don't all remain running the whole time the AC is on, but it seems like most cars' do. All I know is that my car overheats for some reason, even tho the gauge on the dash doesn't indicate that it's running hot. I initially thought it had to be the fan, but I recently started considering the transmission. The issue with the brakes is just something I noticed every time the engine starts running hot and accelerating becomes extremely difficult, to the point where I have to pull over and wait until the car cools down in order to be able to drive normally again. And the brakes still work, by the way, the pedal just feels still when I press it, as if I've pumped them a bunch. If I drive 10 miles from my house, none of these symptoms would occur. It's only after a long distance. I understand my description is all over the place, but I'm just describing exactly what I've been going through. I do plan to take the car to get diagnosed, I was just hoping that maybe someone with the same car and problem could give me some insight before I started spending any major money.