Hello! I have been through your question. According your symptoms and medical history I think this is gastroenteritis most probably caused by a virus ( noroviruses, adenoviruses). A virus is the most common cause of gastroenteritis that is easily spread from one person to another by close contact. This is often because of the virus being present on people s hands after they have been to the toilet, surfaces or objects touched by the infected person can also allow transmission of the virus (infected person prepares food).So, in your case the fact that all the family members have these symptoms in different days and excluding the food poisoning emphasis the above mentioned diagnosis. But, to be sure you should do a stool sample to exclude better the other reasons (bacterial). In this situation I suggest to do re hydration, drinking a lots of fluid(water, tea) and take probiotics. If these symptoms last for more than 3 days and you have fever you should meet a doctor. I hope my answer help you. I wish your family a quick recovery.