It is unlikely that there is much the daycare could have done to prevent the strep throat. Strep throat is very common in children over three, and occurs more frequently in the winter and spring than in the summer. Children pass it on to each other in the same way that they pass on a cold. When there is a case of strep in a classroom, the daycare provider usually sends home a note to the other parents to inform them, so that, if their child starts to have symptoms, it can be diagnosed and treated quickly.
Children with strep need to be on antibiotics for 24 hours before returning to daycare. The incubation period (how long it takes from the time you are exposed until the time you start to show symptoms) for strep is 2-5 days, so it's not absolutely certain that your daughter got strep while in daycare.
Rotavirus is a common occurrence in the winter and spring, as well. It is very contagious. The incubation period for rotavirus is 1-3 days, so it's very likely that your child was exposed to it in daycare. Rotavirus is notoriously common in childcare settings, especially if there are children and infants who are not old enough to be toilet trained. The virus can sit on surfaces and toys. Even with scrupulous cleaning, it can be difficult to control. In addition, rotavirus can be shed in the stool for as long as ten days after the symptoms started, even if the child is back to normal. So, it's hard to know if any particular child is contagious. As an indication of how hard it is to control rotavirus, you should know that it is also the number one cause of diarrhea transmitted in hospitals!
While it would be inappropriate to blame the daycare, it would be reasonable for you to review their infection control guidelines. For example, learn what their standard procedures are for changing diapers, cleaning surfaces and toys, and handwashing. At this time, there is no reason to contact the Board of Health or notify the other parents. You should also teach your older child good hygiene, focusing on hand-washing after using the toilet and before eating any food, and stop sharing other kids' straws, spoons, etc. Even with these precautions, however, it's very likely that your children will get sick more frequently in their first year of daycare.