MaterialPageRoute goes to a new page without the appbar using it with bottomNavigationBar

I have an app with three routes and uses the bottomNavigationBar to navigate between them. In one of the routes I have a button in the page that will also navigate to one of the pages.

Heres my main page

import 'package:flutter/material.dart';

import 'page_two.dart';
import 'page_three.dart';

void main() {
  return runApp(MyApp());
}

/// This Widget is the main application widget.
class MyApp extends StatelessWidget {
  static const String _title = 'Flutter Code Sample';

  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      title: _title,
      home: MyStatefulWidget(),
    );
  }
}

class MyStatefulWidget extends StatefulWidget {
  MyStatefulWidget({Key key}) : super(key: key);

  @override
  _MyStatefulWidgetState createState() => _MyStatefulWidgetState();
}

class _MyStatefulWidgetState extends State<MyStatefulWidget> {
  int _selectedIndex = 0;

  List<Widget> _widgetOptions = <Widget>[
    Text('Main'),
    PageTwo(),
    PageThree(),
  ];

  void _onItemTapped(int index) {
    setState(() {
      _selectedIndex = index;

    });
  }

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        title: const Text('BottomNavigationBar Sample'),
      ),
      body: Center(
        child: _widgetOptions.elementAt(_selectedIndex),
      ),
      bottomNavigationBar: BottomNavigationBar(
        items: const <BottomNavigationBarItem>[
          BottomNavigationBarItem(
            icon: Icon(Icons.home, color: Colors.black),
            title: Text('Home'),
          ),
          BottomNavigationBarItem(
            icon: Icon(Icons.business, color: Colors.black),
            title: Text('Business'),
          ),
          BottomNavigationBarItem(
            icon: Icon(Icons.business, color: Colors.black),
            title: Text('Business'),
          ),
        ],
        currentIndex: _selectedIndex,
        selectedItemColor: Colors.amber[800],
        onTap: _onItemTapped,
      ),
    );
  }
}

Page Two

import 'package:flutter/material.dart';

import 'main.dart';

class PageTwo extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return Container(
      child: RaisedButton(
        child: Text('Go page 1'),
        onPressed: () {
          Navigator.push(
            context,
            MaterialPageRoute(builder: (context) => MyApp()),
          );
        },
      ),
    );
  }
}

and Page Three with a button that navigates to page two

import 'package:flutter/material.dart';

import 'page_two.dart';

class PageThree extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return Container(
      child: RaisedButton(
        child: Text('Go page 1'),
        onPressed: () {
          Navigator.push(
            context,
            MaterialPageRoute(builder: (context) => PageTwo()),
          );
        },
      ),
    );
  }
}

When I press the button on Page Three, it will go to Page Two without the AppBar and the BottomNavigationBar

Solution

Use GlobalKey and In PageTwo Widget call MyStatefulWidgetState's _onItemTapped function
You can see working demo and full code below
code snippet

final scakey = new GlobalKey<_MyStatefulWidgetState>();
...
child: Text('Go page 2'),
    onPressed: () {
      scakey.currentState._onItemTapped(1);

full code

import 'package:flutter/material.dart';

void main() {
  return runApp(MyApp());
}

final scakey = new GlobalKey<_MyStatefulWidgetState>();

/// This Widget is the main application widget.
class MyApp extends StatelessWidget {
  static const String _title = 'Flutter Code Sample';

  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      title: _title,
      home: MyStatefulWidget(key: scakey),
    );
  }
}

class MyStatefulWidget extends StatefulWidget {
  MyStatefulWidget({Key key}) : super(key: key);

  @override
  _MyStatefulWidgetState createState() => _MyStatefulWidgetState();
}

class _MyStatefulWidgetState extends State<MyStatefulWidget> {
  int _selectedIndex = 0;

  final myKey = new GlobalKey<_MyStatefulWidgetState>();

  List<Widget> _widgetOptions = <Widget>[
    Text('Main'),
    PageTwo(),
    PageThree(),
  ];

  void _onItemTapped(int index) {
    setState(() {
      _selectedIndex = index;
    });
  }

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      key: myKey,
      appBar: AppBar(
        title: const Text('BottomNavigationBar Sample'),
      ),
      body: Center(
        child: _widgetOptions.elementAt(_selectedIndex),
      ),
      bottomNavigationBar: BottomNavigationBar(
        items: const <BottomNavigationBarItem>[
          BottomNavigationBarItem(
            icon: Icon(Icons.home, color: Colors.black),
            title: Text('Home'),
          ),
          BottomNavigationBarItem(
            icon: Icon(Icons.business, color: Colors.black),
            title: Text('Business'),
          ),
          BottomNavigationBarItem(
            icon: Icon(Icons.business, color: Colors.black),
            title: Text('Business'),
          ),
        ],
        currentIndex: _selectedIndex,
        selectedItemColor: Colors.amber[800],
        onTap: _onItemTapped,
      ),
    );
  }
}

class PageTwo extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return Container(
      child: RaisedButton(
        child: Text('Go page 1'),
        onPressed: () {
          Navigator.push(
            context,
            MaterialPageRoute(builder: (context) => MyApp()),
          );
        },
      ),
    );
  }
}

class PageThree extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return Container(
      child: RaisedButton(
        child: Text('Go page 2'),
        onPressed: () {
          scakey.currentState._onItemTapped(1);
          /*Navigator.push(
            context,
            MaterialPageRoute(builder: (context) => PageTwo()),
          );*/
        },
      ),
    );
  }
}