Yes, dogs can and do become infected with Clostridium difficile. It is actually more common in dogs than humans, but thankfully is usually easier to treat. Dogs are usually treated with Flagyl or Tylosin (gram neg antibiotics). If your dog presents with an acute case of diarrhea, it is probably time to take her (and a fecal sample) to your vet. They will float the sample in solution and look for evidence of a bacterial overgrowth. Strangely enough, in vet med we call it clostriduim, but human side it is refered to as c-diff.
You may want to contact your vet and let her know you have a possible infection, but I suspect that she won't prescribe antibiotics to all three dogs unless they present with GI distress. It can be a hard line to manage, trying to keep the little creatures healthy while protecting the public health by not over prescribing antibiotics.
Dogs are usually not the disease vector for human infections, but you may want to be extra diligent about washing your hands and grooming tools.
(*disclaimer - I am not your veterinarian, and this isn't medical advice*)