Electrical – Interface of HC05 Bluetooth module and RF 433Mhz Module

I am trying to make an Android controlled toy car. Now the range of the bluetooth module is around 10 meters. However, to increase the range, I decided to interface the RF module with the Bluetooth (HC-05) Module. I have a TX and Rx pair of 433 Mhz. Basically, the app sends an integer value to the Bluetooth module. The Tx pin of the bluetooth module is connected to the Data pin of the transmitter.

On the Receiver side, I have connected the data pin of the receiver to the Rx pin (PIN 0) on the Arduino. This is the overall setup. I have attached an Image of the connections. It's my first time using Fritzing, so please dont mind the nasty connections.

I power the HC-05 and Tx pair using a separate 5V and the Rx using the Arduino. For the sake of the image, I have shown all of the components being powered from the Arduino. I am first testing the whole thing on an LED, so the code attached is that for an LED.
Below is my code:

int LED= 13;  
char input;  

void setup() 
{  
  Serial.begin(9600);  
  pinMode(LED, OUTPUT);  
  Serial.println(">> START<<");  
 }  

 void loop() 
{  
  if(Serial.available()>0)  
    {  
     input= Serial.read();  
     if(input=='1')  
       {  
        Serial.println("ON");  
        digitalWrite(LED, HIGH);  
        delay(2000);  
        }  
     else if(input=='0')  
       {  
        Serial.println("OFF");  
        digitalWrite(LED, LOW);  
        delay(2000);  
        }  
     else  
      {  
      Serial.println("NO INPUT");  
      Serial.println(input);  
      }  
     }  

    }  

Now, without the RF module, that is, when I connect the Tx of the HC-05 to the Rx of the Arduino (PIN 0), the above code works perfectly. However, when I connect the Tx pin of the HC-05 to the Data pin of the Transmitter module and the Data pin of the Receiver module to the Rx pin (PIN 0) of the Arduino, everything goes awry. Any suggestions on why this might be happening?