Disney requests no shorts in the dining room, this applies to children and adults. Infants and toddlers of course would be an exception, but both of these boys are past those stages.
As far as formal night at minimum they should be in dress pants, dress shirt and tie, with dress shoes. JC Penney often ahs sales that you can pick up a smart outfilt with a shirt, tie, vest and pants for under $25. I've seen suits for $25 after Easter as well. Payless and Wal-Mart both have children's dress shoes for around $10.
On Tropical nights shorts and tropical shirts are fine.
Anne