There are couple of ways to connect to a SQL Server using SMO with SQL authentication:

Method 1, create and pass a SQL Connection object to the SMO.Server constructor:

$con = new-object ("Microsoft.SqlServer.Management.Common.ServerConnection") "MyServer\Myinstance","sa","mypassword"
$server = new-object ("Microsoft.SqlServer.Management.Smo.Server") $con

Method 2, first create an SMO.Server object and then set

$server = New-Object ('Microsoft.SqlServer.Management.Smo.Server') "MyServer\Myinstance"
$server .ConnectionContext.LoginSecure = $false
$server .ConnectionContext.Login = "sa"
$server .ConnectionContext.Password = "mypassword"

I noticed you are using the SQL 2008 invoke-sqlcmd cmdlet, SQL authenication is also supported see get-help invoke-sqlcmd and use the -username and -password parameters.