Sure, you can. Beaches and Cream does not take them, but everywhere else does.
Your family might enjoy the character breakfast at Cape May Cafe at the Beach Club. If you like seafood, they have a great buffet at night at the same place. There are many non seafood items as well.
Over on the Boardwalk, our favorite place is Spoodles. You see a lot of families in there. If you want a great steak, I suggest the Yachtsman Steakhouse.