Well, as far as the age limit goes, I am not sure how strict they are. It may depend on the manager for that ship. On the Mariner, we ate at Chops and our daughters ages 13 and 11 (12 next week) ate in the normal dinning room with our table mates (who said they did a very good job of being adults while there) because we didn't want to break the "age rule" for our 11 year old. We were dissapointed when the table next to us had a very obviously younger boy (guestimate at 10 yrs) eating dinner. I don't have a problem with a younger child being there if they behave, but this boy was talking very loudly, getting in and out of his chair and in general not acting in a manner appropriate to the resturant. Our daughters could have very well gone and enjoyed steak with us and been better behaved.
So, the question you SHOULD be asking (and I mean no offense to you or your childern here) is "Are my childern going to act properly in Chops or will they disrupt other diners that may have gone to Chops for a child free atmosphere?" If you can not say yes to the above question, then you should not even ask Chops to "bend the rule". If you say no, you can always take them to the buffet before your reservation and then enjoy yourselves at Chops while they go off to their activities.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013