Kitchen,
I use the desktop icon for start. It is shortcut to MOHW.exe, yes.
After double click on it, origin is starting, dropping back to background and then the launch screen pops up like this:

- MoHW launch screen
Here I simply click launch which starts MoHW, pressing enter, choosing Multiplayer, and I reach the in-game lobby.
It's not that fast at my computer but works reliable. This is also the way I meant when I said "start via origin" because origin is running in background.
If this way doesn't work at your computer, there is something wrong locally, it HAS TO WORK! Even better than through battlelog. So either some windows stuff or the MoHW installation... can't say. You told about a windows problem today, perhaps it is somehow related.