Add library to SharePoint sites using power shell

Will work on your sites three, run from your top site.

$sites = Get-SPWeb <site url>
foreach ($site in $sites.webs)
{
 $listTemplate = $Site.ListTemplates["Document Library"];
 $Site.Lists.Add(<Library name>,<Library Name>,$listTemplate);
 $list = $Site.Lists[<Library Name>];
 $list.Title = <Library Title>;
 $List.DefaultItemOpen = "PreferClient";
 $list.EnableVersioning = $true;               
 $list.EnableMinorVersions = $false;
 $list.MajorVersionLimit = 0;        
 $list.ForceCheckout = $true;
 $List.OnQuickLaunch = $true;
 $List.ContentTypesEnabled = $true
 $list.Update()
 $ctToRemove = $list.ContentTypes[<Main Content Type>]
 $list.ContentTypes.Delete($ctToRemove.Id)
 $list.Update()
 $SPWeb1 = Get-SPWeb -Identity <Main Site where content type is>
 $ctToAdd = $SPWeb1.ContentTypes[<Content Type Name>];
 $ct = $List.ContentTypes.Add($ctToAdd);
 $list.Update()
 $Site.Dispose() 
 $SPWeb1.Dispose()
}