I use http://android-developers.blogspot.jp/2015/05/android-design-support-library.html with SupportMapFragment and Button.
Why can't I see the button on the SupportMapFragment?

activity_main.xml
<?xml version="1.0" encoding="utf-8"?>
<android.support.v4.widget.DrawerLayout xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:app="http://schemas.android.com/apk/res-auto"
    android:id="@+id/drawer_layout"
    android:layout_height="match_parent"
    android:layout_width="match_parent"
    android:fitsSystemWindows="true">
    <include layout="@layout/include_list_viewpager"/>
    <android.support.design.widget.NavigationView
        android:id="@+id/nav_view"
        android:layout_height="match_parent"
        android:layout_width="wrap_content"
        android:layout_gravity="start"
        android:fitsSystemWindows="true"
        app:headerLayout="@layout/nav_header"
        app:menu="@menu/drawer_view"/>
</android.support.v4.widget.DrawerLayout>
map_fragment.xml with SupportMapFragment
<?xml version="1.0" encoding="utf-8"?>
<RelativeLayout xmlns:android="http://schemas.android.com/apk/res/android"
    android:layout_width="match_parent"
    android:layout_height="match_parent">
    <fragment xmlns:android="http://schemas.android.com/apk/res/android"
        android:id="@+id/map"
        class="com.google.android.gms.maps.SupportMapFragment"
        android:layout_width="match_parent"
        android:layout_height="match_parent" />
    <Button
        android:id="@+id/start_button"
        android:layout_width="match_parent"
        android:layout_height="wrap_content"
        android:layout_alignParentBottom="true"
        android:text="start"
        />
</RelativeLayout>
include_list_viewpager.xml
<?xml version="1.0" encoding="utf-8"?>
<android.support.design.widget.CoordinatorLayout
    xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:app="http://schemas.android.com/apk/res-auto"
    android:id="@+id/main_content"
    android:layout_width="match_parent"
    android:layout_height="match_parent">
    <android.support.design.widget.AppBarLayout
        android:id="@+id/appbar"
        android:layout_width="match_parent"
        android:layout_height="wrap_content"
        android:theme="@style/ThemeOverlay.AppCompat.Dark.ActionBar">
        <android.support.v7.widget.Toolbar
            android:id="@+id/toolbar"
            android:layout_width="match_parent"
            android:layout_height="?attr/actionBarSize"
            android:background="?attr/colorPrimary"
            app:popupTheme="@style/ThemeOverlay.AppCompat.Light"
            app:layout_scrollFlags="scroll|enterAlways" />
        <android.support.design.widget.TabLayout
            android:id="@+id/tabs"
            android:layout_width="match_parent"
            android:layout_height="wrap_content" />
    </android.support.design.widget.AppBarLayout>
    <android.support.v4.view.ViewPager
        android:id="@+id/viewpager"
        android:layout_width="match_parent"
        android:layout_height="match_parent"
        app:layout_behavior="@string/appbar_scrolling_view_behavior"
        />
</android.support.design.widget.CoordinatorLayout>
Thank you.
                        
I think problem lies in your map_fragment.xml with SupportMapFragment. Try below.