Retailers are being very careful with coupons these days. I've had to figure out Joann's policies over the past few months. First of all, our store does take competitors coupons, and as long as your purchase matches the coupon, they will take it. As far as the overall discount, the coupons usually state that you cannot combine a coupon and this discount. If an item is on sale, usually the overall discount applies. This has been my experience. Since I work retail, I find Joann's to be very generous with their coupons and shop there before I would go to Michael's or AC Moore.
I used to shop for most of my crafting needs at AC Moore, but then they changed their policy and I asked them, what is the motivation for shopping here as opposed to Joann's? I understood that I was only talking to a cashier, and I asked her to pass the message on. I have a teacher discount for most of these stores, and Joann's is, BY FAR, the best deal.
Speak directly to a manager so they can explain what coupons and discounts apply where and how, or, if you think your Joann's is not following their rules, email or call the company.