Your link to the offer on the Disney Food blog is one that's been available for quite a while. In fact booking it ends today. It's very possible that it's sold out at your resort and/or for the days your Mother wants it. So, the CM would be correct that she cannot get it under those circumstances.
I didn't see any mention of Sept 15 or 16 (you mentioned different dates on your posts), but I didn't check the Canadian site for special offers. However, if that offer requires check in by Sept 15 or 16 then arriving on Sept 23 would not qualify.
If adding your Mother would not exceed the allowable capacity of your room, you could add her to your room and she would be able to get FD. If she's the third adult there would be an additional nightly fee + the same length of ticket.