#include <SoftwareSerial.h>
#include "Arduino.h"
#include <TinyGPS.h>
#include <SoftwareSerial.h>
Maybe you need to include SoftwareSerial.h several more times.
// Define which pins you will use on the Arduino to communicate with your
// GPS. In this case, the GPS module's TX pin will connect to the
// Arduino's RXPIN which is pin 3.
#define RXPIN 2
#define TXPIN 3
SoftwareSerial mySerial(7, 8);
Well, which is it? Pins 2 and 3 or pins 7 and 8?
// Initialize the SoftwareSerial library to the pins you defined above
SoftwareSerial uart_gps(RXPIN, TXPIN);
Never mind. I see. You are trying to use two instances of SoftwareSerial. I recommend that you find a padded wall to keep banging your head against.
Get a Mega.