The short answer: call Emirates and ask them. Now. Time is short.
The long answer: I’m part of an Emirates Skywards “my family” account myself and I had no idea that points from credit cards can’t be pooled. But now that I’ve looked at Emirates’ website, I’m not so sure: over and over again, they talk about “points from flights” and they never talk about anything else. So you may be on to something!
I’m also wondering whether if you want to share your points, another FF programme might be a better fit for you? Have you looked into KrisFlyer (for Star Alliance flights) or Asia Miles (for Oneworld flights)? Their family sharing system seems to be a little more flexible than Emirates, and you’ll also be able to find flights with them where the taxes and surcharges are lower than Emirates’. You may well have already looked into this and have decided that Emirates is indeed best for your situation – in which case, all good. But if you haven’t, I’d seriously consider one of the other programmes.
I hope this helps. Now go and call Emirates and let us know what they say!