It’s not the answer you want to hear, but from what you’re describing, the issue is probably the motor inside the door panels. When using the interior buttons, the locks work fine, but with the key fob, it doesn’t have enough power, and the old motor can’t do its job. Trust me, if you change it, you’ll see what I mean. 
@Teddy
The only thing I don’t get is that all doors lock/unlock without any problems using the interior buttons. Maybe I’m missing something.
Sky said:
@Teddy
The only thing I don’t get is that all doors lock/unlock without any problems using the interior buttons. Maybe I’m missing something.
I can’t explain it, man. I’m a noob when it comes to electronics. But I had the exact same issue with my 1999 Explorer. A guy from a forum in Germany who’s a pro at Explorers sent me some used but working actuators after I described my problem. I swapped them out and it was fixed.
Maybe the fob uses a different power source or relay with less juice, which just isn’t enough for a 25-year-old worn-out actuator 
. Like I said, I don’t know for sure.
@Teddy
If nothing else works, I might give that a shot. It’s an old vehicle after all.
Sky said:
@Teddy
If nothing else works, I might give that a shot. It’s an old vehicle after all.
Yep 
. Rockauto has good options with all the needed screws. Watch a how-to video before swapping it out though. It can get a bit tricky.
Check eBay. They might have a factory service manual for your car. If it’s a multi-volume set, one of those volumes could have the diagram you’re looking for.