i think it could be an allergic reaction from something you all use in your house or something you have all been eating. try cutting things out and see if you notice any change. you could all have a genetic problem. ask your doctor if you can be reffered to a specialise e.g. a dermatologist who specializes in skin or a dieticion who could help figure out if you are all eating something that could be allergic to you. good luck.
Gymdandee is spot on.
Get the name of a GOOD allergist (often tied to a hospital) and the name of a GOOD dermatologist. See whoever you can first.
Make notes of all changes in your lifestyle/household. For instance a new detergent as Gymdandee rightly queries could be responsible for your family's rashes AND the dog's if the dog has come into contact with any washing.
Also, have you purchased any new furniture or furnishings such as pillows, curtains, towels or bed linen? They may have allergy producing ingredients in them.
Have you changed your laundry detergent, body soap, something new in food ?
I suggest you go to a Dermatologist and or an Allergist