IC is not known as a family friendly brand, are you stuck with that one or are you willing to use other IHG brands?

Having looked for hotel rooms for 5 in UK/France (nearly impossible to find for less than the cost of just getting 2 rooms) I noticed how few rooms there were even for 4. The ages of course matter, and the age of what is a "child" vs "adult" varies from country to country.

I suspect that you will be stuck with contacting hotels individually. I was successful getting another hotel chain (curiously, in EDI) to take more than the booking engine allowed by contacting them directly. Although that ended up being stressful on arrival because those notes were lost in the system (but I had printed out emails to show).