How do I include both a left and right sidemenu in ionic?

This actually is very simple. You just need to have two side-menus, and two corresponding buttons that will toggle the side menus.

E.g :

    <ion-side-menus>
        <ion-side-menu-content>
            <ion-nav-bar class="bar-dark">
                <ion-nav-back-button class="button-icon ion-arrow-left-c">
                </ion-nav-back-button>
            </ion-nav-bar>
            <ion-nav-buttons side="left">
                <button class="button button-icon button-clear ion-navicon" menu-toggle="left">
                </button>
            </ion-nav-buttons>
            <ion-nav-buttons side="right">
                <button class="button button-icon button-clear ion-navicon" menu-toggle="right">
                </button>
            </ion-nav-buttons>
            <ion-nav-view name="appContent"></ion-nav-view>
        </ion-side-menu-content>
        <ion-side-menu side="left">
            <ion-header-bar class="bar-assertive">
                <h1 class="title">Left Menu</h1>
            </ion-header-bar>
            <ion-content>
                <ion-cart ng-controller='CartController'></ion-cart>
            </ion-content>
        </ion-side-menu>
        <ion-side-menu side="right">
            <ion-header-bar class="bar-assertive">
                <h1 class="title">Right Menu</h1>
            </ion-header-bar>
            <ion-content>
                <ion-cart ng-controller='CartController'></ion-cart>
            </ion-content>
        </ion-side-menu>
    </ion-side-menus>

You can refer to the complete codepen here