Or just post the TV value itself and avoid having to load modx in your mailer script.
Use a hidden field in your form:
<input type="hidden" name="email" value="[[*email_tv]]" id="contact_email_tv" >
In your js, change this section as follows:
// FORM SUBMISSION
$('.button.btSend.css3button').click(function(){
//Get name field value
var frmName = $('#contact_name').val();
//Get e-mail field value
var frmMail = $('#contact_email').val();
//Get phone field value
var frmPhone = $('#contact_phone').val();
//Get company field value
var frmCompany = $('#contact_company').val();
//Get textarea message
var frmMessage = $('#contact_message').val();
// ADDED: Get hidden email_tv field value
var frmEmail = $('#contact_email_tv').val();
//Send data using ajax
$.post("/mail.php", {action: "sendMail", name: frmName , mail: frmMail, phone: frmPhone, company: frmCompany, message: frmMessage, email: frmEmail}, // <--- added frmEmail
Then in your php file you can the email tv value with:
$email = $_POST['email'];
I might have missed something in your js file but pretty sure that should do it...
Note: my suggestion in this post would work fine if your js was embedded instead of in an external file (hadn't realised that was the case)