MS Word loads the available styles from Endnote Web when you open the program, so to add an additional style you will need to:
1. Close Word
2. Open Endnote Web
3. In EW, choose FORMAT/BIBLIOGRAPHY
4. Click on Select Favorites
5. Scroll down and find "Author-Date", click to highlight it and "Copy to Favorites"
6. Open your Word document. Click on Endnote Web tab
7. Choose Author-Date from the Style drop-down menu
That should fix the order problem while keeping them in Author-Date format.