How to access a database that is used by a sharepoint site

Body
Hi guys. I'll be rather brief if I can so here goes.
I made this app in C# that goes onto my employee portal and automatically gets my shifts for me every 30 minutes my using a web browser control and then it reads the HTML data from that and generates a calendar for me and also provides automated alerts.

Issue
Problem is that this web browser uses IE (yeesh help me) and it doesn't work with all parts of the site. I have done some digging around on the site and I found where the ASP site gets the data from: An XML sheet somewhere on the server. I can access this XML sheet, but only if I'm logged in (please see the attached images for more information).

Current solution
So my question is this: How do I actually login to this area?
I could login using the webbrowser and then download the XML using that, but it's too slow and too old, so is there a way I can pass my credentials through? The URL is like this "https://www.mycoles.com.au/api/rosters/nextweek" -- I don't see any thing like ?name=myname ?pass=mypassword... soo yea. (I'm a bit new).

Further details:
Application language: C#
Current technology: Windows forms applications/ IE web browser control
Site backend: Microsoft Sharepoint
Anything I'm missing? Please ask..?

Attached content
Mycoles XML Logged in
Mycoles XML Access Denied