As a non-chemical solution (I'm guessing you're trying to avoid them because of the dog), lay some black plastic over the beds you're trying to rid of weeds for a week or so. The plastic will absorb the heat from the sun killing many weeds while depriving them from the sunlight needed for photosynthesis as a double whammy. Then rake out the mulch, put down some landscape/weed block fabric and put back the mulch. Obviously if there are desirable plants or bushes in the bed you don't want to cover them with the plastic.

__________________

1980 300TD-China Blue/Blue MBTex-2nd Owner, 107K (Alt Blau) OBK #15
'06 Chevy Tahoe Z71 (for the wife & 4 kids, current mule) '03 Honda Odyssey (son #1's ride, reluctantly) '99 GMC Suburban (255K+ miles, semi-retired mule) 21' SeaRay Seville (summer escape pod)