Q:

I don't believe Angular UIrouter is routing to my view

Not changing to the correct template via ui-view when I click on the button in my footer to route to that view. Console is not spitting out any errors, so I am baffled. 
Here are my states
$stateProvider
                .state("home", {
                    url: "/home",
                    templateUrl: "src/templates/home.html",
                    controller: "ListController as ul"
                })
                .state("home.about", {
                    parent: "home",
                    url: "/about",
                    templateUrl: "src/templates/home/about.html"
                })
                .state("home.archived", {
                    parent: "home",
                    url: "/archived",
                    templateUrl: "src/templates/home/archived.html"
                });

and here is my footer which is hosting a menu with links to the ui-sref states.
<nav role="navigation" class="navbar navbar-default navbar-fixed-top">
<ul class="footerul">
<li class="footerlist"><md-menu>
    <md-button class="menu" aria-label="Open demo menu" class="md-icon-button" ng-click="$mdOpenMenu($event)">
        <i class="fa fa-cog fa-lg"></i><span> Menu</span>
    </md-button>
    <md-menu-content width="6">
        <md-menu-item>
            <md-button ui-sref="home" ng-click="{ active: nav.isActive('/home')}">
                <i class="fa fa-home"></i>
                Home
            </md-button>
        </md-menu-item>
        <md-menu-item>
            <md-button ui-sref="home.about" ng-click="{ active: nav.isActive('/about')}">
                <i class="fa fa-info-circle"></i>
                About
            </md-button>
        </md-menu-item>
        <md-menu-item>
            <md-button ui-sref="home.archived" ng-click="{ active: nav.isActive('/archived')}">
                <i class="fa fa-info-circle"></i>
                Archived
            </md-button>
        </md-menu-item>
    </md-menu-content>
</md-menu></li>

everything was routing correctly until I put in the parent key into my states and added about and archived as children of home.

A:

The way you have currently implemented a state will result into some wiered state name formation, like about child state will be accessible with name home.home.about and archived state would be accessible as home.home.archived, which is happened due to injection of parent: 'home' option in your state definition. which appends parent state name before the child state name.
Basically you shouldn't mix up two approaches of defining child state, below are the approaches to define child state.

Define parent attribute in your state definition
follow dot(.) notation while defining child state, like parentState.childState

Lets look at how could you fix it.
You should remove the parent attribute from all child states, as you already followed the 2nd way(followed dot notation to define child state)
OR
If you wanted to stick with the parent option on state then state configuration will look like below.
Config
$stateProvider
.state("home", {
  url: "/home",
  templateUrl: "src/templates/home.html",
  controller: "ListController as ul"
})
.state("about", {
  parent: "home",
  url: "/about",
  templateUrl: "src/templates/home/about.html"
})
.state("archived", {
  parent: "home",
  url: "/archived",
  templateUrl: "src/templates/home/archived.html"
});

