can you post the coupon?
first off the $3 for the ink cartridge IS a coupon. you cannot use 2 coupons in the same transaction. some stores are more lenient, but overall that is the policy.
i'm not sure wha t$10 coupon you're referring to, but I recall one that was a single use coupon that everyone and their brother was using and the managers sometimes caved and honored it and sometimes didn't. if it's a one time use coupon you should not be surprised if it was not honored. There was also a coupon that was good for only a specific store in new jersey. if you used that one and did not use it at that store in new jersey then you should not be surprised they did not accept it.
if you had a valid $10 coupon then they should have taken the $10 off instead of the $3 (one coupon per transaction)