Transistors with different grounds?

Hey!

I'm trying to interface my car's key fob with my arduino. The problem is that the key fob doesn't have a common ground... Rather it has a common 10VDC+ line. The button is being "pushed" when the 10VDC+ line is shorted with one of the multiple grounds. I thought this would be an appropriate usage for transistors. I'm using NPN ones by the way.

I'm able to get one button working well with the arduino when it is hooked up like this:
(Please excuse my handwritten schematic... I think all the symbols are right.)

But when I try to hook up two buttons. The key fob doesn't lock or unlock my car! The light on the key fob lights up, but it is acting like I'm pressing both buttons at once. (from what I can assume) I even added diodes to keep the ground lines from connecting.

I have code that is just similar to the blink code, but it just alternates between the buttons. It shouldn't impact the functionality of this though because my issues aren't software related. I'll post it anyways.

int lockPin = 5;
int unlockPin = 6;

void setup()
{
  Serial.begin(9600);
  delay(100);
  Serial.println("Program Starting Up!");
}

void loop()
{
  Serial.println("Locking Car");
  digitalWrite(lockPin, HIGH);
  delay(1000);
  digitalWrite(lockPin, LOW);
  
  Serial.println("===============");
  delay(3000);
  
  Serial.println("UNLOCKING car");
  digitalWrite(unlockPin, HIGH);
  delay(1000);
  digitalWrite(unlockPin, LOW);
  
  Serial.println("===============");
  
  delay(10 * 1000);
 
}

Anyways, I'm hoping that I can interface 4 buttons (lock, unlock, remote start, and trunk) to the Arduino. I'd be appreciative if you could give me ideas on how to wire these up using smaller components. I thought transistors would be ideal until I found out that it has a common anode. I'd rather not have to use relays because of the size / price, but I would if it is an absolute last resort.

Thanks for your help!
-Mitch

The keyfob functions are actuated by getting (touching) +10 over to one of the terminals (lock or unlock)?
Or is that those get taken to ground?

I'm a big proponent of using 5V reed relays for such things (replicating switch functions.)

Yes, the key fob functions are actuated by touching +10 over to one of the terminals. When I tapped them with my multimeters, the +10VDC seemed to be common, but the terminals (lock, unlock) all were negative. They were all separated all the way down to the IC on the fob.