It may be possible to shift the order of the home menu via CSS but it would not be easy.
You can explore the options in this article: StackOverFlow - Reorder using CSS
At one level I can understand why you might want to change the order but the "Home" menu is relative to the currently selected database, so intuitively, it should follow the "Database" menu.
Therefore I often choose a name for the Home menu such as "Expense Home", or "Finance Home".
If the user only has access to a single Database then they would not see the "Database" menu item.
