Software serial conflict with WiFi on ESP8266
As noted, there are conflicts between Wifi and SoftwareSerial. The attempt in the question to disconnect WiFi is a step in the right direction, but not enough. You have to actually turn off the WiFi. The challenge is to reliably shut down the WiFi and then start it up again. This has been discussed extensively in the ESP8266/Arduino Git repository here and is referred to by some as "Issue 644".  An sample implementation of the code to reliably is presented here. 

Here's what the on/off functions look like. I strongly urge you to go to the code linked above and copy from there rather than here, though.

extern "C" {
#include "user_interface.h"
#define WIFI_RETRIES 25

int conn_tries = 0;
bool WiFiOff() {
    WiFi.disconnect();
    WiFi.mode(WIFI_OFF);
    WiFi.forceSleepBegin();
    yield();

    /* 
     * It can take a while for the ESP to disconnect, so we need
     * to give it a couple of seconds before returning a fail.
     */
    while ((WiFi.status() == WL_CONNECTED)
           &amp;&amp; (conn_tries++ &lt; WIFI_RETRIES)) {
        delay(100);
#ifdef DEBUG
        Serial.print(".");
#endif
    }
    if (WiFi.status() != WL_CONNECTED)
        return (true);
    else
        return (false);
}

/*
 * Turn the WiFi back on again with forceSleepWake().
 * NOTE:-  =Your= SSID and password must be in the
 *         user_config.h file.
 */
bool WiFiOn() {
    conn_tries = 0;


    WiFi.forceSleepWake();
    WiFi.mode(WIFI_STA);
    wifi_station_connect();
    WiFi.begin("corazon_del_bosque", "");

    /* 
     * It may take a while for the ESP to re-connect, depending
     * upon external factors (e:- has the access-point moved out
     * of range since we were last connected?).  This loop will
     * give us a reasonable time to re-connect without blocking
     * permanently.
     */
    while ((WiFi.status() != WL_CONNECTED)
           &amp;&amp; (conn_tries++ &lt; WIFI_RETRIES)) {
        delay(100);
#ifdef DEBUG
        Serial.print(".");
#endif
    }
    if (WiFi.status() == WL_CONNECTED)
        return (true);
    else
        return (false);
}


I'm using this code in my program via the Arduino IDE. The author used it in PlatformIO. Other build systems may have other requirements.