I would say to Ilana before you try to convince your sister-in-law of anything, you could acquaint yourself with aphorism 165.
There is just no point in prescribing homoeopathic medicines based on non-characteristic common symptoms, like nausea, lassitude, headache, cough, congestion. There is no guarantee that you will increase your odds by combining additonal remedies in a complex. Homoeopathy works by symptom similarity based on a small number of characteristic individualizing symptoms in the case.
Some people hold the view that if, by luck, the right remedy is amongst all the others that some good will come out of it. There is an inherent danger in this type of thinking. Should the case become complicated with sequalae you are really going to need to access all the information from known remedy relationships to bring the case back on track. Combinations like these make this more difficult to achieve and since we are in the business of attempting to cure quickly, safely and gently then where is the integrity?
Why does she desperately want to keep her children cold-free anyway? This doesn't make any sense. A healthy immune response is a godsend, it is not wise to suppress all natural immune function, this only leads to possible deeper pathology later on.

These types of acute conditions are self-limiting anyway. I think that's how the companies who sell these type of OTC products get away with their false advertising.