Much of the required behaviour can be achieved by configuring your mail software. The details vary considerably between products and you should consult the product documentation or present your requirements very carefully to any contractors managing your mailers.

It is unfortunate that in many cases the default behaviour (the way the software works as delivered or following a standard installation, upgrade or patch) is to openly relay, so you should check after making any changes.

The Janet relay tester service may be helpful at that stage.