As you know, there are numerous causes of hives: infectious, allergic, chemical, foods, insect stings, physical (solar, heat, cold), etc. For your daughter, the precipitating cause may well be viral infections and there is no preventative for the overwhelming majority of viral infections.
Your best bet would be to seek consultation at an academic institution, with resources dedicated to treatment and research on hives. One such would be the National Jewish Medical and Research Center. Your daughter's allergist might be able to recommend another.
Good luck.
I'm a stay at home mom with a similar (but not exact) experience to your daughter, so take my suggestion for what it's worth.
I had chronic hives since childhood. It was undiagnosed until my 20s. My new allergist said people with dermagraphism (my form of chronic hives) was frequently a side symptom of an auto-immune disease. He tested me for 6 different ones, and I came back positive for Hashimotos (my immune system attacks my thyroid).
Point being, my immune system had issues/body in distress/chemicals out of whack - hence the hives.
Hives are caused from too much Histamine (both "histamine 1" and "histamine 2") being release by the body, as I'm sure you know. He put me on Zyrtec and Zantac. Zantac is the only histamine 2 blocker on the market that he knows about, and Zyrtec is a H1 blocker. Taken together they did cure my hives...but when I tried to go off of them, my body went into shock and so much histamine was released that I was a swollen walking hive from head to toe. ouch. but I refused to drug myself that much each day (and it cost $100 a month for me to afford the meds...so, I had to stop).
The good news was that by my taking Synthroid for my thyroid disease, my hives became a very mute issue within 3 months. My body was back in balace and the hives stayed at bay.
I suggest this because your daughters immune system is in distress when she is sick. So, when her body is distressed, her body produces too much histamine. What the exact connection is, I don't know. Hope something triggers an idea for you though. At the least, you could ask your doc for a prescription of at least Zantac and Zyrtec, so she has something to take when she is sick.
Best to you.