Others are posting that they don't see why you wanted his help, but wasn't it because you also had your son with you and wanted dad to deal with son so you could focus on daughter?.....
When you have calmed down (and yeah, I'd be furious right now too), and a day or so has passed, you and he need to talk without the kids around or demanding your attention.
"We need to talk now, when the kids are not sick and it's not a sudden emergency. Now--not when a kid is sick or one of us is sick and we're rushing around--now is the time to come up with our rules about how we're both going to operate the next time this happens. Because, husband, it IS going to happen again; kids will get sick again at inconvenient times for you AND for me. Or a kid will get hurt at school and need to go to the doctor or even the hospital. Or for other reasons, we'll need to act like a team, all on the same page and the same side, which you and I did not do at all the other day."
Then you and he need to agree on what the procedure will be. He needs to understand: You have TWO children, so if an emergency doctor visit is needed for one of them, you really do not want to have both of them there; it is distracting to the parent trying to hear a doctor's instructions and exposes the well child to germs, etc. If you need to get daughter to a doctor, husband leaves work and gets son and takes him home -- as someone else posted, there was absolutely no reason for your husband and son to sit in the waiting room today! And husband will be responsible for food,period. If YOU are the one picking up the well child, while he goes to the doctor, YOU will be responsible for food. And so on.
Tell him how you feel but don't be accusatory: Try "I feel" statements: "When I call you at work and tell you our child is vomiting and I need help, I feel devalued when I'm told that you cannot come." "When we have been struggling just to get a vomiting child to stop vomiting and to see the doctor, I feel angry and upset when I hear that I am also expected to have dinner plans for us." And so on.
If this is a pattern with him, and he is generally unhelpful with the kids and does not understand obvious things like "we don't take a vomiting, feverish child out to eat," he and you really do need to talk more and he needs to see the reality of things. HE should spend a day with the vomiting child next time and should be responsible for all cleaning up, disinfecting (he clearly worries about contagion so he should learn what an antibacterial wipe is and where to use it around the house) and so on.
Oh, and I agree with the person posting that you should not have sent your child to day care or anywhere else the day after the first fever showed. I figure that since she has very seldom been ill, you probably did not even realize the 24-hour rule: No school, preschool or day care wants a child back unti the child has been fever-free for at least 24 hours. You can see the reason why in your own experience -- the fever going down due to medications, and the child seeming fine, does not mean the illness is anywhere near over.