Doing what you want to do is going to be a little work. You can embed the Family Echo website in your website with an iframe. But there's really no substitute for sending people individual links so that they can either (a) edit their own details of (b) create an account and edit the whole tree.
If I was going to do this, I think I would use the tree itself as an incentive. Something like, "I'll send you an email with a link, so that you can see the tree and edit the information". That way you don't have to send out a whole bunch of individualized links to people who might have no interest in a family tree.
As always, if you share editing access to your tree, be sure to make backups of your GEDCOM file on a regular basis (and check the tree history).