Changing the behavior of the publish button is not recommeded and will just end up confusing everyone. Also adding a new button will just lead to more confusion about which button your editors should be using.
Since your editors have to use workflow, they probably don't need access to the standard publish button. Simply removing them from the Sitecore Client Publishing role will make it so they can't see the publish button and therefore have to use the workflow command.
If workflow is turned on, a new version of an item will always be put into the first step of that workflow. You could change that behavior with a handler for the version:added event. If you are only concerned about new items, a processor for the uiAddFromTemplate pipeline could also be used. However, I don't recommend changing this behavior at all. For that matter, I don't recommend using full admin users for content editing at all since you will lose the versioning of your content items. Admin users should be used for administration, not content editing.