Custom password/reset service

Correct. In the second script, you would again call the password reset/forgot email endpoint and send the new template.

To reset user/password:
POST user/password?reset=true
{"email":"youremail@yourdomain.com"}

OR
POST user/password
{"email":"youremail@yourdomain.com","reset":true}

To create a new template

POST http://{url}/api/v2/system/email_template

Request Body:

{
    "resource": [
        {
            "name": "",
            "description": "",
            "to": "",
            "cc": "",
            "bcc": "",
            "subject": "",
            "body_text": "",
            "body_html": "",
            "from_name": "",
            "from_email": "",
            "reply_to_name": "",
            "reply_to_email": ""
        }
    ]
}

In other words, once you have a new template setup, you can simply call that template from your second script using the name of the template - /api/v2/system/email_template_name

Refer this link to learn more about email templates: Setting up email templates - DreamFactory