I'm not a plumber, but I'll try to get you started:
- washer needs a 2" trap and standpipe. The 1.5" is too small
- the washer line needs to then dump into a 3" or larger vertical or horizontal branch (this is in 2006 IPC and should also be in the 2009 version)
- reducing the pipe size in the direction of flow (the 1.5" to the 1.25" reducer in the pic) is not a good idea. The 1.25" is also really too small for the washer
- the current setup doesn't properly vent the sink. When the washer runs, it'll pull the water out of the sink trap
Probably the easiest solution is to just put the washer hose into the utility sink. Since the utility has some storage capacity, the line does not have to be 2". We'll see what the pros think.