This is a touchy subject and you will get answers for yes and no.
If you go by the written dress code Disney has the answer would be no. No shorts or tank tops for anyone accept with a pirate costume on pirate night.
How ever you do see many young kids in nice dress shorts at dinner.
They wont say anything to you and of course your still going to sit down and have dinner. But it is against their dress code.
The Wonder is much more lax in their dress than the Magic.
I guarantee you will see adults in shorts and jeans at dinner too, even though they request that you dont wear them. I fyou watch you will see every manner of clothing.
So its up to you to decide.
I know the resoning for their rules is to make it a bit nicer atmosphere for dinner for those who like to dress properly for dinner. This means alot to some people and seeing shorts or tank tops ruins it for them. I don't think it is too much to ask of people just for dinner to wear long pants.
But i also understand who wants to buy nice long pants for little kids who will out grow them by the end of the cruise or never wear them again.
Personally i have no problem with kids in shorts at dinner as long as they are nice shorts, not the torn up looking ones that many like to wear. Formal night might be a different story.
If your not sure you do have another option. are your kids old enough for the clubs? If so you can sign them up to go with the club to dinner during your dinner time and then stay and play until your done.
They take them to a kid friendly buffet and plenty of counselors to help them with trays and reaching foods.
If they are small and not potty trained you can always try to reserve the nursery during your dinner time. There is an extra charge for that. It use to be $6 per hur, 2 hour minimum.
Just depends if you want a family dinner or a adult dinner just for the 2 of you for a nice change. Most younger kids love to eat with the clubs. That way they arnt sitting for 90 minutes while course after course is served at dinner. They love choosing what they want, eating with kids and then getting to go back and run and play in the club.
On a 7 day we did it both ways with the grandkids , although all of them preferred eating with the club.
hope that helps you some,
Kathleen