are you submitting to a form library in sharepoint or just email? if you are submitting to a form library, then in yoru data connection you have to select overwrite files if it already exists. It will not allow the form to submit if you do not have this selected and keeping the same form name.
I assume it is your workflow that isn't sending out the second email? If that is the case, then you need it to check or work from changes on the form. Maybe put on the form, a hidden box that you assign values to when you submit. For example, first person it would submit 1, your workflow would wait for that text box to equal one, then it would execute those actions. The second person would assign the value of 2 when click submit, your workflow would wait for that text box to equal one, then it would execute those action and end workflow.
You can do it with sharepoint designer easily. If you need robust... visual studio 2005. You have to develop those workflows on the machine that MOSS is installed on.