It is fine to use your own form but you still need the add to cart server behavior code on the page. You can modify it to work with your own form though. If you want to have Universal Email on the page and an add to cart you should have the Universal Email occur first, then the add to cart afterwards.
The add to cart server behavior will take you to the cart page if you specify this when applying it to the page. This should be where you start, you can then update the add to cart server behavior to work with your own form.
Are you able to get the item adding to the cart and the email sent? If so you should be ok to just add in a redirect to your cart page. Please post back with these details and include a copy of the page in question so we can see what is going on with it.