Dear Barbra,
This little boy is only two and one-half. He should not be expected to do things for very long, nor to be able to show much adeptness yet at solving problems. It sounds like his development is proceeding a bit unevenly in the cognitive area, but not to any problematic extent.
The aggression toward his sibling needs to be monitored carefully, and he should be placed in time out immediately if he displays any aggression toward her. He should be supervised at all times, but this would be true of any two-year-old.
sounds like he is a bit jealous of the baby. A new member of the family can be a big change for a 2yr old. Have her get games that will help his motor and cognitive skills. Try games that take lots of physical activity such as duck, duck, goose. Set aside a time of day that is all his like the baby's nap time and devote all your attention to him.
What does she feed him? Have her eliminate artificial dyes, flavors and preservatives from his diet. Cook from scratch and use no preprocessed foods. No Jello, Kool-aid, limit juices, sugar, sodas, and candy. No junk food, only raw veggies and fruits for snacks.
Also try Omega-3 and Omega-6 fatty acids. We use Efalex but it is kind of expensive. You can use flax oil but will have to supplement with DHA.
This poor child is too young to be on medication since none are approved for kids under 6. Does the mother give him attention and play with him? That helps a lot.
Time outs, yelling and spanking will not help. Specific praise for good behavior works. It takes about two weeks to see improvement but it does work. Plus talking calmly about why he should not hit and what the appropriate behavior is helps too.
My 5 yr old was just like this a year and a half ago. He does not hit any more, no tantrums, and his hyperactivity is almost nill. It comes back when he eats certain foods. We limit dairy products also. Allergy tests can be helpful in determining what foods cause the hyperactivity, but the blood test is better than the ***** test in determining food allergy.